Gluon scattering amplitudes and two-dimensional integrable systems
|
|
- Alexandra Powell
- 6 years ago
- Views:
Transcription
1 Gluon scattering amplitudes and two-dimensional integrable systems Yuji Satoh (University of Tsukuba) Based on Y. Hatsuda (DESY), K. Ito (TIT), K. Sakai (YITP) and Y.S. JHEP 004(200)08; 009(200)064; 04(20)00 ; Y. Hatsuda (DESY), K. Ito (TIT) and Y.S. JHEP 202(202)003; arxiv:2.6225, to appear in JHEP
2 . Introduction gauge/string duality AdS/CFT correspondence string theory in 4D maximal AdS space super Yang-Mills dual strong/weak (λ: coupling) [AdS: anti-de Sitter] [CFT: conformal field theory] discovery of integrability opened up new dimensions
3 gauge/string duality beyond susy sectors quantitative analysis of gauge theory dynamics at strong coupling
4 gauge/string duality beyond susy sectors quantitative analysis of gauge theory dynamics at strong coupling stimulating study of SYM insights into applications.
5 In fact, spectrum of planar AdS/CFT for arbitrary coupling [Gromov-Kazakov-Vieira 09, Bombardelli-Fioravanti-Tateo 09, Arutyunov-Frolov 09,...] given by thermodynamic Bethe ansatz (TBA) eqs. ( finite size effects of 2D integrable models ) checked up to 5/6-loops of SYM [Bajnok-Hegedus-Janik-Lukowski 09,... ] ( 4 loops Feynman diagrams )
6 In fact, spectrum of planar AdS/CFT for arbitrary coupling Also, [Gromov-Kazakov-Vieira 09, Bombardelli-Fioravanti-Tateo 09, Arutyunov-Frolov 09,...] given by thermodynamic Bethe ansatz (TBA) eqs. ( finite size effects of 2D integrable models ) checked up to 5/6-loops of SYM other aspects? [Bajnok-Hegedus-Janik-Lukowski 09,... ] ( 4 loops Feynman diagrams ) gluon scattering amplitude/wilson loops [this talk] correlation fn. quark - anti-quark potential/cusp anomalous dim..
7 gluon scatt. amplitudes at strong coupling minimal surfaces in AdS5 x S5 thermodynamic Bethe ansatz (TBA) equations [ AdS/CFT ] [ integrability ]
8 In this talk, discuss maximally helicity violating (MHV) amplitude/ Wilson loops of 4D maximal ( N =4 ) SYM at strong coupling underlying 2D integrable models and CFTs derive analytic expansions around certain kinematic points [ regular polygonal Wilson loops ]
9 Plan of talk. Introduction 2. Gluon scattering amplitudes at strong coupling 3. Minimal surfaces in AdS and integrability 4. Analytic expansion of amplitudes at strong coupling 5. Summary [ amplitude min. surface ] [ min. surface Hitchin system, TBA ] [ AdS3 case, AdS4 case ]
10 k4 2. Gluon scattering amplitudes at strong coupling x4 amplitudes of SYM at strong coupling x x3 x2 k2 N =4 M = AdS/CFT [Alday-Maldacena 07] minimal surfaces in AdS M : scalar part of MHV amplitudes λ : t Hooft coupling null boundary at AdS boundary x µ i+ x µ i =2 kµ i n-pt. amplitude e p 2 (Area) (momentum of particle) n-cusp min. surface
11 4-cusp solution (4-pt. amplitude) AdS5 is parametrized in R 2,4 as Y Y := Y 2 Y Y 2 + Y Y Y 2 4 = string e.o.m. eq. of min. surface Y ( Y Y ) Y =0 ( Y ) 2 =( Y ) 2 =0 ( = z, = z ) simple solution AdS3 Y + Y 4 Y + Y 0 Y Y 0 Y Y 4 Y 2 = Y 3 = 0, z = + i = p 2 e + e e + e
12 Poincare coordinates Y µ = xµ r (µ =0,, 2, 3) Y + Y 4 = r, Y Y 4 = r2 + x µ x µ r ) ds 2 = r 2 dr2 + dx µ dx µ [ r 0 : AdS boundary] boundary coord. of AdS3 : x ± = Y 0 ± Y Y + Y 4 2 Z 3 4
13 regularizing area, e.g., by 4! 4 2 M 4 apple M div 4 exp 8 f( ) ln s t 2 + const. f( )= p / [cusp anom. dim] s, t : Mandelstam variables precisely matches BDS conjecture [all orders in perturbation] f( ) : exactly same as in spectral problem [Bern-Dixon-Smirnov 05]
14 Insights into SYM amplitudes min. surface Wilson loop Remainder fn. : deviation from BDS formula dual conformal symm. remainder fn. = fn. of cross-ratios of cusp. coord. x µ a
15 Insights into SYM amplitudes min. surface Wilson loop Remainder fn. : deviation from BDS formula dual conformal symm. remainder fn. = fn. of cross-ratios of cusp. coord. x µ a amplitude at strong coupling geometrical object
16 cf. 2-loop 6-pt. remainder fn. [Del Duca-Duhr-Smirnov 09] R (2) 6,W L (u,u 2,u 3 )= (H.) ( ) u 2 24 π2 G, u u + u 2 ; + ( ) 24 π2 G, ; + ( ) u u + u 2 24 π2 G, ; + ( ) u u + u 3 u 3 24 π2 G, u 2 u 2 + u 3 ; + ( ) 24 π2 G, ; + ( ) u 2 u + u 2 24 π2 G, ; + ( ) u 2 u 2 + u 3 u 24 π2 G, u 3 u + u 3 ; + ( ) 24 π2 G, ; + ( ) u 3 u + u 3 24 π2 G, ; + ( u 3 u 2 + u G 0, 0, ), ; + 32 ( u u + u G 0, 0, ), ; + 32 ( 2 u u + u G 0, 0, ), ; + ( 3 u 2 u + u G 0, 0, ), ; + 32 ( u 2 u 2 + u G 0, 0, ), ; + 32 ( 3 u 3 u + u G 0, 0, ), ; ( 3 u 3 u 2 + u 3 2 G 0,, 0, ) ( ; + G 0, ), 0, ; 2 ( u u 2 u u + u G 0,, 0, ) ; + ( 2 u u 3 G 0, ), 0, ; 2 ( u u + u G 0,, ), ; 2 ( 3 u u u + u G 0,, ), ; ( 2 u u u + u 3 2 G 0,, ), ; 2 ( u u 2 u + u G 0,, ), ; 2 ( 2 u u 3 u + u G 0,, 0, ) ; + ( 3 u 2 u G 0, ), 0, ; 2 ( u 2 u + u G 0,, 0, ) ( ; + G 0, ), 0, ; ( 2 u 2 u 3 u 2 u 2 + u 3 2 G 0,, ), ; 2 ( u 2 u u + u G 0,, ), ; 2 ( 2 u 2 u 2 u + u G 0,, ), ; ( 2 u 2 u 2 u 2 + u 3 2 G 0,, ), ; + 4 ( ) u 2 u 3 u 2 + u G u 2 0, 3 u + u 2, 0, ; + ( ) u 4 G u 2 0, u + u 2,, 0; 4 ( ) u G u 2 0, u + u 2,, ; + ( ) u 4 G u 2 0, u + u 2,, ; 4 ( ) u u G u 2 0, u + u 2, u 2 u + u 2, ; ( u 2 G 0,, 0, ) ; 2 ( u 3 u G 0,, 0, ) ( ; + G 0, ), 0, ; + ( u 3 u 2 u 3 u + u 3 G 0, ), 0, ; 2 ( u 3 u 2 + u G 0,, ), ; 2 ( 3 u 3 u u + u G 0,, ), ; ( 3 u 3 u 2 u 2 + u 3 2 G 0,, ), ; 2 ( u 3 u 3 u + u G 0,, ), ; + ( 3 ) u 3 u 3 u 2 + u 3 4 G u 0, u + u 3, 0, ; + 4 ( ) u G u 0, 3 u + u 3,, 0; ( ) u 3 4 G u 0, u + u 3,, ; + 4 ( ) u G u 0, 3 u + u 3,, ; ( ) u 3 u 3 4 G u 0, u + u 3, u u + u 3, ; + 4 ( ) u G u 3 0, 3 u 2 + u 3, 0, ; + ( ) u 2 4 G u 3 0, u 2 + u 3,, 0; 4 ( ) u G u 3 0, 2 u 2 + u 3,, ; + ( ) u 2 u 3 G 0,,, ; ( ) u 3 u 3 G 0,,, ; [ heroic effort ] continues 7 pages...
17 w/ a little more heroic effort... [Goncharov-Spradlin-Vergu-Voloich 0] R 2-loop 6 = 3 i= L 4 (x + i,x i ) 2 Li 4( /u i ) 2 Li 2 ( /u i ) J J amplitude at strong coupling sum up all-orders
18 3. Minimal surfaces and integrability difficult to construct min. surfaces w/ null bound. for n 5 [cf. special 6-cusp sol., Sakai-Satoh 09] but possible to obtain A(area) w/o explicit solutions [Alday-Maldacena 09] string e.o.m. Hitchin system patching 4-cusp sol. amplitudes TBA eq. [Alday-Gaiotto-Maldacena 09, Hatsuda-Ito-Sakai-YS 0 Alday-Maldacena-Sever-Vieira 0]
19 Let us see this for 2n-cusp min. surface in AdS3 4D external momenta in # of cusps : even in AdS3 R, [mom. conservation] 2 light-cone coord. x ± at (AdS)
20 Pohlmeyer reduction [evolution of moving frame] basis in R 2,2 AdS 3 : q =( Y, Y, Y, N) T N a = 2 e abcdy b Y c Y d, e 2 = 2 Y Y string e.o.m. evolution eq. of q : (d + U)q =0 so(4) su(2) su(2) introducing spectral parameter ζ 0= d + B( ), B z = B z = linearized eq. 2 e e p 2 p = p(z) := 2 e p e Y N
21 compatibility/flatness cond. set B z = A z + z, B z = A z + z ) D z z = D z z = 0, F z z +[ z, z] =0 [ su(2) Hitchin system ] e 2 + p(z) 2 e 2 =0 [ generalized sinh-gordon ] original solution Y Y aȧ = + Y 2 Y + Y 0 Y Y 0 Y Y 2 = ( = )M ( = i) =(, 2) ; M : certain matrix
22 2n-cusp solution change of variables dw = p pdz, ˆ = 4 ln p ˆ 2 sinh ˆ =0 [ sinh-gordon ] ˆ =0 4-cusp sol. in w-plane take p(z) =z n 2 + [polynomial] ) w z n 2 ( z ) solution w/ ˆ! 0 ( w ) : 2n-cusp sol. in z-plane Z 2 W n/2 times 3 4 [no explicit form]
23 Cross-ratios [ how to obtain physical info. w/o explicit sol. ] in each (i-th) quadrant in w-plane ( ; w) =b i ( ; w)+s i ( ; w) b i /s i : big/small sol. ew/ + w 0, e 0 (w/ + w ) can show cross-ratios are given by Stokes data x ± ij x± kl x ± ik x± jl = (s i ^ s j )(s k ^ s l ) ( ) [ =, ±i for +, ] (s i ^ s k )(s j ^ s l ) s i ^ s j := det (s i,s j ); x µ i,i+ := xµ i+ x µ i =2 kµ i shape of min. surface cross-ratios/momenta
24 Finding cross-ratios define T- and Y- fn. by T 2k+ =(s k ^ s k+ ), T 2k =(s k ^ s k ) [+] Y s = T s T s+ [ cross-ratios] where f [a] ( ):=f(e a i/2 ) identities among det (s i ^ s j )(s k ^ s l )=(s i ^ s k )(s j ^ s l )+(s i ^ s l )(s k ^ s j ) T [+] s T [ ] s = T s+ T s + Y [+] s Y [ ] s =(+Y s )( + Y s+ ) (s =,..., n-3 ) [T-system] [Y-system]
25 asymptotics for ζ 0, by WKB for Hitchin system log Y s Z s (! 0) etc. Z s = H s p pdz [ s : cycle on alg. curve] (asymptotics) + (analyticity) log Y s = m s cosh + X r K sr log( + Y r ) = e,m s =2Z s [for real Zs] K sr = I sr / cosh, I sr = s,r+ + s,r Y 0 = Y n 2 =0
26 Computing area amplitudes regularization of area (Area) =4 Z d 2 ze 2! 4 Z d 2 z (e 2 p p p)+4 Z r d 2 z p p p A free = X s Z =: A free + A reg d 2 m s cosh log( + Y s ). remainder fn. R (remainder fn.) = A A BDS = A free +
27 Summarizing so far, TBA eqs. to compute AdS3 amplitudes (2n-pt.), need to solve log Y s ( )= m s cosh + r K sr log( + Y r ) Y Y Y 4 Y 7 7 n = 7 Ys : (extended) cross-ratios of e.g. ) Y i 2 = x + 5 x+ 67 x + 56 x+ 7 x ± a, Y 0) = x 5 x 67 x 56 x 7 m s : complex param. shape of surface momenta Ksr Isr (incidence mat. of An-3)
28 Summarizing so far, TBA eqs. to compute AdS3 amplitudes (2n-pt.), need to solve log Y s ( )= m s cosh Y Y Y 4 Y 7 7 n = 7 r K sr log( + Y r ) TBA eq. of hom. sine-gordon model Ys : (extended) cross-ratios of e.g. ) Y i 2 = x + 5 x+ 67 [Hatsuda-Ito-Sakai-YS 0] x + 56 x+ 7 x ± a, Y 0) = x 5 x 67 x 56 x 7 m s : complex (mass) param. shape of surface momenta Ksr Isr (incidence mat. of An-3)
29 Remainder function [overall coupling dependence : omitted] Once Y-fn. are obtained R 2n := A [amp.] - A BDS [ n odd ] [BDS formula] = 7 2 (n 2) + A periods + A BDS + A free 7 A periods = 4 m r I rs m s c 6 = x 23 x 45 x 6 x 2 x 34 x 56 A BDS = 4 n i,j= log c+ i,j c + i,j+ log c i,j c i,j, c ± i,j = x± i+2,i+ x± i+4,i+3 x± j,i x ± i+,i x± i+3,i+2 x± j,j A free = n 3 s= d 2 m s cosh log( + Y s ( )) free energy of TBA system non-trivial part : A free, A BDS for given ms
30 4D amplitude at strong coupling 2D integrable systems 0D superstring
31 Solving TBA eqs. exact solutions { m s m s 0 : CFT limit regular polygon TBA system : solved numerically
32 Solving TBA eqs. exact solutions { m s m s 0 : CFT limit regular polygon TBA system : solved numerically [but sometimes simple iteration fails] solutions to TBA system : not fully investigated momentum dependence : ms momentum
33 Solving TBA eqs. exact solutions { m s m s 0 : CFT limit regular polygon TBA system : solved numerically [but sometimes simple iteration fails] solutions to TBA system : not fully investigated momentum dependence : ms momentum Analytic results at strong coupling except m s! 0,?? we discuss expansions around CFT lim. l = ML 0 ( m s = M s L = M s ML) [ M: mass scale, L: length scale ]
34 4. Analytic expansion at strong coupling [Hatsuda-Ito-Sakai-YS, Hatsuda-Ito-YS ] Basis of expansion TBA for AdS3 2n-pt. amplitude HSG from bsu(n 2) 2 [bu()] n 3 [w/ imaginary resonance param.] [Hatsuda-Ito-Sakai-YS 0] relation between T-fn. and g-function (boundary entropy) [Bazhanov-Lukyanov-Zamolodchikov 94; Dorey-Runkel-Tateo-Watts 99; Dorey-Lishman-Rim-Tateo 05]
35 Homogenous sine-gordon (HSG) model start w/ coset CFT bsu(n) k /[bu()] N [Fernandez Pousa-Gallas-Hollowood-Miramontes 96] [ for 2n-cusp AdS3 min. surface N = n-2, k=2 ] HSG model : integrable deformation of coset CFT S HSG = S gwznw + d 2 x Φ : comb. of weight 0 adjoint op. = = N N + k, = M 2( ) [multi-param. deformation] simplest case from bsu(2) k /bu() complex sine-gordon/minimal A k affine Toda
36 spectrum [copies of min. affine Toda] k- a k Ms a = sin M s, sin k M s = M M s a N- M M 2 s M N min. surface 2D integrable model CFT
37 Expansion of Afree : [ R 2n A free + A BDS ] free energy around CFT limit CFT perturbation for the case of 2n-cusp min. surface in AdS3 A free = 6 c n + f bulk n + c n = k=2 f (k) n (n 2)(n 5) n fn bulk = 4 m r Irs f (k) n k-pt. fn.of m s l 4k n [central charge]
38 A BDS : ( c ± ij ) can show cross-ratios c ± ij : nothing but T-fn. [ trans. matrix] c + ij = T [i+j] i j (0), c ij = T [i+j+] i j (0) where T [k] s ( ):=T s + i 2 k ) A BDS = A BDS (T s ) everything fits into language of 2D integrable model
39 T-function g-function g-fn. log G (0) Z = e RH = (boundary entropy) R integral eq. for g-fn. is known : similar to TBA eq., including boundary contributions k=0 [Dorey-Lishman-Rim-Tateo 05; Poszgay 0; Woynarovich 0] comparing this w/ TBA eq. following G (k) (l) 2 e RE k [Dorey-Runkel-Tateo-Watts 99; Dorey-Lishman-Rim-Tateo 05] [counts ground state degeneracy] L G (0) s,c. G (0) = T s i 2 C
40 boundaries reflection factors : trivial boundary R s,c > r s, C : ( R r s,c ( ) = R r ( ) Z s,c r ( ) [deforming factor] [Sasaki 93] need to find Z s,c r satisfying boundary bootstrap, unitarity, crossing symm. corresponding precisely to T s ) Z s,c r ( ) := ( + C) ( C) sr (x) := sinh 2 ( + i 2 x) sinh 2 ( i 2 x)
41 Expansion of T-function periodicity [ T-system ] T s ( )= t (p,q) s l ( )(p+q) cosh 2p n p,q=0 boundary CFT perturbation of g-fn. t (2,0) s t (0,0) s t (0,0) s = = ng( M j )B( 2, ) sin( 3(s+) 2(2 ) 2 sin( (s+) n ) sin (s+) n sin( n ), [Dorey-Runkel-Tateo-Watts 99; Dorey-Lishman-Rim-Tateo 05] n ) s sin( n ) sin( 3 n ) (z) (0) = G2 ( M s ) z 4 s sin( 3 n )! sin( n ) [ given by modular S-matrix ] t (2,0) s,t (0,4) t (2,0) s T-system ng( M s )
42 Expansion of 2n-pt. remiander function Combining all, R 2n = R (0) 2n + l 8 (4) n R 2n fn. of := t (2,0) s + O(l 2 n ) R (0) 2n = 4n (n 2)(3n 2) n 2 2 R (4) 2n = 6 C(2) n t (2,0) A n,s + t (0,0) s t (2,0) s t (0,0) s 2 + t(2,0) s t (0,0) s 2 2 t (2,0) s t (0,0) s C (2) n = 3(2 ) 2(n 4) n 2 n 2 n 2 ng 2 ( M j ) ng( M s ) n 4 4 (n 3)/2 X s= (n 3)/2 X s= sin( (s+) log 2 n ) sin( s n ) cos regular polygon (2,0) t (n 3)/2 A n,s 2 t (0,0) (n 3)/2 2 n 2 4 t(0,4) s t (0,0) s 4 n n (2,0) 2t s t(2,0) s, t (0,0) s t(0,0) s t (0,4) s t (0,0) s 2 sin n log t(0,0) s t (0,0) s (x) = (x)/ ( x)
43 To further express amplitudes by momenta need ng, n, m s [mass-coupling/relevant op. relation] invert relation btw Y-fn. (cross-ratio) and m s ) m s = m s (k a ) [k a : momenta]
44 To further express amplitudes by momenta need ng, n, m s [mass-coupling/relevant op. relation] invert relation btw Y-fn. (cross-ratio) and m s ) m s = m s (k a ) [k a : momenta] this can be done for single mass cases simpler TBA of perturbed coset [Zamolodchikov 95; Fateev 94] e.g.) M s = s, M ) su(2) su(2) n 3 su(2) n 2 = M n,n M s =( s, + s,n 3 )M [minimal models] ) su(2) su(2) n/2 2 su(2) n/2 = M n 2,n
45 amplitudes along certain trajectories in momentum space CFT/regular polygon-lim.
46 8-pt. remainder function [simplest for AdS3] A integral representation of 8-pt. remainder fn. HSG model Ising model all order expansion in l 2 [Alday-Maldacena 09] R 8 = k=0 R (2k) 8 ( )l 2k R (0) 8 ( ) =5 4 R (2) 8 ( ) = 8 log log 2 6 R (4) log 2 8 ( ) = [ l = ML, m = le i ] + 2 log (3) 92 3 cos 4 [Hatsuda-Ito-Sakai-YS 0]
47 0 pt. remainder function For 0-pt., these completely fix ng, m s R 0 = R (0) 0 + R(4) 0 l8/5 + O(l 2/5 ) R (0) 0 = log2 2 cos 5 R (4) 0 = 5 tan 5 + C t (2,0) = C 2 ( M 4/5 + C = 20 cos t (2,0) 2 4/5 2/5 M 2 C 3 M [ l = ML, m s = M s l ] complex regular polygon M 2/5 2 ) 5 /2 log 2 cos 5 C 2 = /5 0 cos 4 6 /5 5 3 /5 C 3 =2 2 /4 4/5 3/5 4/5 /2
48 M - =M- 2 = 2M - =M- 2 = 0M - =M- 2 = R CFT lim. l ( = /20, 2 = /5 ) l- dependence of 0-pt. remainder function [ m s = M s le i s ] dashed lines : R (0) 0 + R(4) 0 l8/5 good agreement w/ numerics
49 comparison w/ analytic results at two loops [Heslop-Khoze 0] rescaled remainder fn. : close for all 2n-pt. amplitudes
50 5. AdS4 minimal surfaces and W minimal models [ Hatsuda-Ito-YS, to appear ] Amplitudes at strong coupling for momenta R,2 min. surface in AdS4 Y-system for AdS4 m-cusp sol. [Alday-Maldacena-Sever-Vieira 0] Y 2,s Y 2,s + = ( + Y 2,s+)( + Y 2,s ) Y,s Y 3,s ( + Y,s )( + Y 3,s ) Y 3,s Y,s + = ( + Y 3,s+)( + Y,s Y 2,s +Y 2,s ) Y,s Y 3,s + = ( + Y,s+)( + Y 3,s Y 2,s +Y 2,s ) Y,s = Y 3,s Y ± a,s ( )=Y a,s ( ± m - 5 i), s =,...,m 5
51 TBA for AdS4 m-pt. amplitude HSG from bsu(m 4) 4 [bu()] m 5 simple iteration for numerics near CFT lim. does not seem to work, generally analytic expansion near CFT lim. : possible [cf. Castro Alvaredo-Fring 04]
52 single mass cases AdS3 case: su(2) cosets n-3 AdS4 case: su(4) cosets in particular, 2 3 m - 5 M s = s, M ) su(4) su(4) m 5 su(4) m 4 = WA (m,m) 3 M s =( s, + s,m 5 )M [W-minimal models] su(4) su(4) m/2 5 su(4) m/2 4 ) = WA (m 2,m) 3
53 6-pt. remainder function [simplest for AdS4/5] [cf. Alday-Gaiotto-Maldacena 09] HSG model Z4 parafermion CFT deformed by one relevant op. [no mixing] expansion near CFT limit agrees w/ partially numerical results in [Hatsuda-Ito-Sakai-YS ] rescaled remainder fn. : close to 2-loop result
54 7-pt. remainder function similarly to 0-pt. for AdS3, mass-coupling relation is completely determined R 7 = R (0) 7 + R (4) 7 l 6/7 + O(l 24/7 ) R (0) 7 = R (4) 7 = C + C2 2 G 2 applelog 2 2 cos 7 2 cos Li 2 2 cos [ l = ML, m s = M s l ] regular polygon G = M 8/7 + M 8/7 2 + C 3 M 4/7 M 4/7 2 C = C 2 = 2(2 ) 2/7 2 (3/7) (/7) B(/7, 3/7) 2(2 ) /7 sin 3 7 sin 3 7 s sin 4 sin 5 4 s sin 5 4 sin 4! C 3 = /4 apple 4 6 /2 apple ( 7 8 ) ( 3 4 ) ( 5 8 ) 8/7 2
55 CFT lim l = 40, 2 = 20 l- dependence of 7-pt. remainder function dashed lines : R (0) 7 + R (4) 7 l6/7 good agreement w/ numerics (points) [ m s = M s e i s l ]
56 AdS5 case [Alday-Maldacena-Sever-Vieira 0] Y-system for AdS5 m-cusp sol. [ momenta R,3 ] Y 2,s Y 2,s + = ( + Y 2,s+)( + Y 2,s ) Y,s Y 3,s ( + Y,s )( + Y 3,s ) Y 3,s Y,s + = ( + Y 3,s+)( + Y,s Y 2,s +Y 2,s ) Y,s Y 3,s + = ( + Y,s+)( + Y 3,s Y 2,s +Y 2,s ) 2 3 m - 5 Y,s 6= Y 3,s Y couples to on l.h.s.,s Y 3,s [ non-standard Y-system] underlying integrable model: not identified yet
57 7. Summary N =4 Gluon scatt. amplitudes of SYM at strong coupling minimal surfaces in AdS [ AdS/CFT ] TBA equations [ integrability ]
58 7. Summary N =4 Gluon scatt. amplitudes of SYM at strong coupling minimal surfaces in AdS TBA equations [ AdS/CFT ] [ integrability ] Underlying 2D integrable (HSG) model analytic expansions of amplitudes/wilson loops around CFT lim. [regular polygon] A free bulk CFT perturbation A BDS T-function T-/Y-fn. g-fn. boundary CFT perturbation
59 Why minimal surface TBA? [cf. ODE/IM] T-function g-function (boundary entropy)? Why strong coupling 2 loops : close [ full structure of amplitudes ] General AdS5 case? Strong coupling corrections? [cf. Alday-Gaiotto-Maldacena-Sever-Vieira 0].
60 4D N =4 SYM 0D string on AdS5 x S5 2D integrable system CFT [ λ: t Hooft coupling ]
Gluon Scattering Amplitudes from Gauge/String Duality and Integrability
Gluon Scattering Amplitudes from Gauge/String Duality and Integrability University of Tsukuba Yuji Satoh based on JHEP 0910:001; JHEP 1001:077 w/ K. Sakai (Keio Univ.) JHEP 1004:108; JHEP 1009:064, arxiv:1101:xxxx
More informationSix-point gluon scattering amplitudes from -symmetric integrable model
YITP Workshop 2010 Six-point gluon scattering amplitudes from -symmetric integrable model Yasuyuki Hatsuda (YITP) Based on arxiv:1005.4487 [hep-th] in collaboration with K. Ito (TITECH), K. Sakai (Keio
More informationTwo-loop Remainder Functions in N = 4 SYM
Two-loop Remainder Functions in N = 4 SYM Claude Duhr Institut für theoretische Physik, ETH Zürich, Wolfgang-Paulistr. 27, CH-8093, Switzerland E-mail: duhrc@itp.phys.ethz.ch 1 Introduction Over the last
More informationNew insights in the amplitude/wilson loop duality
New insights in the amplitude/wilson loop duality Paul Heslop Amplitudes 2010 6th May based on 0910.4898: Brandhuber, Khoze, Travaglini, PH 1004.2855: Brandhuber, Katsaroumpas, Nguyen, Spence, Spradlin,
More informationFeynman Integrals, Polylogarithms and Symbols
Feynman Integrals, Polylogarithms and Symbols Vittorio Del Duca INFN LNF based on work with Claude Duhr & Volodya Smirnov ACAT2011 7 September 2011 let us consider l-loop n-point Feynman integrals example:
More informationNikolay Gromov. Based on works with V.Kazakov, S.Leurent, D.Volin F. Levkovich-Maslyuk, G. Sizov
Nikolay Gromov Based on works with V.Kazakov, S.Leurent, D.Volin 1305.1939 F. Levkovich-Maslyuk, G. Sizov 1305.1944 Gauge/Gravity duality July 29- August 2, 2013 Munich, Germany Motion of the string: The
More informationComputing amplitudes using Wilson loops
Computing amplitudes using Wilson loops Paul Heslop Queen Mary, University of London NBIA, Copenhagen 13th August 2009 based on: 0707.1153 Brandhuber, Travaglini, P.H. 0902.2245 Anastasiou, Brandhuber,
More informationSpiky strings, light-like Wilson loops and a pp-wave anomaly
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arxiv:080.039 A. Tseytlin, M.K. arxiv:0804.3438 R. Ishizeki, A. Tirziu, M.K. Summary Introduction
More informationAnalytic 2-loop Form factor in N=4 SYM
Analytic 2-loop Form factor in N=4 SYM Gang Yang University of Hamburg Nordic String Theory Meeting Feb 20-21, 2012, NBI Based on the work Brandhuber, Travaglini, GY 1201.4170 [hep-th] Brandhuber, Gurdogan,
More informationString hypothesis and mirror TBA Excited states TBA: CDT Critical values of g Konishi at five loops Summary. The Mirror TBA
The Mirror TBA Through the Looking-Glass, and, What Alice Found There Gleb Arutyunov Institute for Theoretical Physics, Utrecht University Lorentz Center, Leiden, 12 April 2010 Summary of the mirror TBA
More informationThermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS 3
RIKEN-TH-8 TIT/HEP-60 UTHEP-60 arxiv:00.9 Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS Yasuyuki Hatsuda, Katsushi Ito, Kazuhiro Sakai and Yuji Satoh Theoretical Physics Laboratory,
More informationNikolay Gromov. Based on
Nikolay Gromov Based on N. G., V.Kazakov, S.Leurent, D.Volin 1305.1939,????.???? N. G., F. Levkovich-Maslyuk, G. Sizov, S.Valatka????.???? A. Cavaglia, D. Fioravanti, N.G, R.Tateo????.???? December, 2013
More informationScattering amplitudes and AdS/CFT
Scattering amplitudes and AdS/CFT Cristian Vergu Brown University BOX 1843 Providence, RI 02912 1 Introduction and notation Scattering amplitudes in the maximally supersymmetric N = 4 gauge theory are
More informationHexagon Functions and Six-Gluon Scattering in Planar N=4 Super-Yang-Mills
Hexagon Functions and Six-Gluon Scattering in Planar N=4 Super-Yang-Mills L. Dixon, J. Drummond, M. von Hippel and J. Pennington, 1307.nnnn LMS Symposium, Durham July 8, 2013 All planar N=4 SYM integrands
More informationIntegrability and Finite Size Effects of (AdS 5 /CFT 4 ) β
Integrability and Finite Size Effects of (AdS 5 /CFT 4 ) β Based on arxiv:1201.2635v1 and on-going work With C. Ahn, D. Bombardelli and B-H. Lee February 21, 2012 Table of contents 1 One parameter generalization
More informationAdS/CFT duality, spin chains and 2d effective actions
AdS/CFT duality, spin chains and 2d effective actions R. Roiban, A. Tirziu and A. A. Tseytlin Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2-d actions, hep-th/0604199 also talks
More informationarxiv: v3 [hep-th] 14 Dec 2011
arxiv:1012.4003 overview article: arxiv:1012.3982 Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling Luis F. Alday arxiv:1012.4003v3 [hep-th] 14 Dec 2011 Mathematical
More informationNumerics and strong coupling results in the planar AdS/CFT correspondence. Based on: Á. Hegedűs, J. Konczer: arxiv:
Numerics and strong coupling results in the planar AdS/CFT correspondence Based on: Á. Hegedűs, J. Konczer: arxiv:1604.02346 Outline Introduction : planar AdS/CFT spectral problem From integrability to
More informationMarta Orselli. Based on: hep-th/ , hep-th/ hep-th/ , arxiv: arxiv: , arxiv: work in progress
Marta Orselli Based on: hep-th/0605234, hep-th/0608115 hep-th/0611242, arxiv:0707.1621 arxiv:0806.3370, arxiv:0912.5522 + work in progress IDEA: obtain an understanding of the quantum mechanical nature
More informationMSYM amplitudes in the high-energy limit. Vittorio Del Duca INFN LNF
MSYM amplitudes in the high-energy limit Vittorio Del Duca INFN LNF Gauge theory and String theory Zürich 2 July 2008 In principio erat Bern-Dixon-Smirnov ansatz... an ansatz for MHV amplitudes in N=4
More informationY-system for the Spectrum of Planar AdS/CFT: News and Checks
-,,,,, Y-system for the Spectrum of Planar AdS/CFT: News and Checks Vladimir Kazakov (ENS, Paris) Collaborations with N.Gromov, A.Kozak, S.Leurent, Z.Tsuboi and P.Vieira Outline Integrability for QFT in
More informationThe Steinmann-Assisted Bootstrap at Five Loops
The Steinmann-Assisted Bootstrap at Five Loops Lance Dixon (SLAC) S. Caron-Huot, LD, M. von Hippel, A. McLeod, 1609.00669 New Formulations for Scattering Amplitudes LMU, Munich 5 Sept., 2016 Hexagon function
More informationIntegrability of spectrum of N=4 SYM theory
Todai/Riken joint workshop on Super Yang-Mills, solvable systems and related subjects University of Tokyo, October 23, 2013 Integrability of spectrum of N=4 SYM theory Vladimir Kazakov (ENS, Paris) Collaborations
More informationN=4 Super-Yang-Mills in t Hooft limit as Exactly Solvable 4D Conformal Field Theory
PACIFIC 2014 UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental Interactions September 15-20, 2014, Moorea, French Polynesia N=4 Super-Yang-Mills in t Hooft limit as Exactly Solvable
More informationWilson loops and amplitudes in N=4 Super Yang-Mills
Wilson loops and amplitudes in N=4 Super Yang-Mills Vittorio Del Duca INFN Frascati 7 March 2011 N=4 Super Yang-Mills maximal supersymmetric theory (without gravity) conformally invariant, β fn. = 0 spin
More information2nd Asia-Pacific Summer School in Mathematical Physics, Canberra
1. Wrapping effect 2. Thermodynamic Bethe ansatz method 3. Luscher corrections 4. Y-systems High-order Feynman diagrams connect operators farther away When the length of a composite operator is shorter
More informationANALYTIC SOLUTION OF BREMSSTRAHLUNG TBA BASED ON WITH A.SEVER. IGST2012 Zurich
ANALYTIC SOLUTION OF BREMSSTRAHLUNG TBA BASED ON 1207.5489 WITH A.SEVER IGST2012 Zurich Introduction Big progress in understanding of spectrum of N=4 SYM [Lipatov] [Faddeev,Korchemsky] [Minahan,Zarembo]
More informationTBA Equations for Minimal Surfaces in AdS
Equations for Minimal Surfaces in AdS Katsushi Ito Tokyo Institute of Technology Y. Hatsuda, KI, K. Sakai, Y. Satoh, arxiv:002.294 JHEP 004 (200) 08, arxiv:005.4487 JHEP 009 (200) 064 November 9, 200 @Osaka
More informationProgress in understanding quantum spectrum of AdS 5 S 5 superstring
Progress in understanding quantum spectrum of AdS 5 S 5 superstring Arkady Tseytlin R. Roiban, AT, arxiv:0906.494, arxiv:0.09 M. Beccaria, S. Giombi, G. Macorini, R. Roiban, AT, arxiv:03.570 M. Beccaria,
More informationExact anomalous dimensions of 4-dimensional N=4 super-yang-mills theory in 'thooft limit
PACIFIC 2015 UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental Interactions September 12-19, 2015, Moorea, French Polynesia Exact anomalous dimensions of 4-dimensional N=4 super-yang-mills
More informationSeries Solution and Minimal Surfaces in AdS arxiv: v3 [hep-th] 23 Dec 2009
Preprint typeset in JHEP style - HYPER VERSION BROWN-HET-1588 Series Solution and Minimal Surfaces in AdS arxiv:0911.1107v3 [hep-th] 23 Dec 2009 Antal Jevicki, Kewang Jin Department of Physics, Brown University,
More informationColor-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
Physics Amplitudes Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops Josh Nohle [Bern, Davies, Dennen, Huang, JN - arxiv: 1303.6605] [JN - arxiv:1309.7416] [Bern, Davies, JN
More informationTowards solution of string theory in AdS3 x S 3
Towards solution of string theory in AdS3 x S 3 Arkady Tseytlin based on work with Ben Hoare: arxiv:1303.1037, 1304.4099 Introduction / Review S-matrix for string in AdS3 x S3 x T4 with RR and NSNS flux
More informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationarxiv: v2 [hep-th] 29 May 2014
Prepared for submission to JHEP DESY 14-057 Wilson loop OPE, analytic continuation and multi-regge limit arxiv:1404.6506v hep-th] 9 May 014 Yasuyuki Hatsuda DESY Theory Group, DESY Hamburg, Notkestrasse
More informationFOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS. Lorenzo Magnea. University of Torino - INFN Torino. Pino Day, Cortona, 29/05/12
FOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS Lorenzo Magnea University of Torino - INFN Torino Pino Day, Cortona, 29/05/12 Outline Crossing paths with Pino Cusps, Wilson lines and Factorization
More informationA Brief Introduction to AdS/CFT Correspondence
Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation
More informationMagnon kinematics in planar N = 4 Yang-Mills
Magnon kinematics in planar N = 4 Yang-Mills Rafael Hernández, IFT-Madrid Collaboration with N. Beisert, C. Gómez and E. López Outline Introduction Integrability in the AdS/CFT correspondence The quantum
More informationarxiv: v1 [hep-th] 17 Sep 2010
Preprint typeset in JHEP style - HYPER VERSION arxiv:1009.3428v1 [hep-th] 17 Sep 2010 A numerical test of the Y-system in the small size limit of the ËÍ µ ËÍ µ Principal Chiral Model Matteo Beccaria and
More informationS Leurent, V. Kazakov. 6 July 2010
NLIE for SU(N) SU(N) Principal Chiral Field via Hirota dynamics S Leurent, V. Kazakov 6 July 2010 1 Thermodynaamic Bethe Ansatz (TBA) and Y -system Ground state energy Excited states 2 3 Principal Chiral
More informationAdS/CFT duality. Agnese Bissi. March 26, Fundamental Problems in Quantum Physics Erice. Mathematical Institute University of Oxford
AdS/CFT duality Agnese Bissi Mathematical Institute University of Oxford March 26, 2015 Fundamental Problems in Quantum Physics Erice What is it about? AdS=Anti de Sitter Maximally symmetric solution of
More informationEmergent Gauge Theory
Emergent Gauge Theory (Based on work with JiaHui Huang, Minkyoo Kim, Laila Tribelhorn and Jaco Van Zyl) Robert de Mello Koch South China Normal University and Mandelstam Institute for Theoretical Physics
More informationShort spinning strings and AdS 5 S 5 spectrum
Short spinning strings and AdS 5 S 5 spectrum Arkady Tseytlin R. Roiban, AT, arxiv:0906.4294, arxiv:02.209 M. Beccaria, S. Giombi, G. Macorini, R. Roiban, AT, arxiv:203.570 70-s: origin of string theory
More informationExact spectral equations in planar N=4 SYM theory
Euler Symposium on Theoretical and Mathematical Physics Euler International Mathematical Institute, St. Petersburg, July 12-17, 2013 Exact spectral equations in planar N=4 SYM theory Vladimir Kazakov (ENS,
More informationExact results for Wilson loops in N = 4 SYM
Exact results for Wilson loops in N = 4 SYM Diego H. Correa Universidad Nacional de La Plata - CONICET - Argentina Based on arxives: 1202.4455, 1203.1019 and 1203.1913 In collaboration with: J. Henn, J.
More information10 Interlude: Preview of the AdS/CFT correspondence
10 Interlude: Preview of the AdS/CFT correspondence The rest of this course is, roughly speaking, on the AdS/CFT correspondence, also known as holography or gauge/gravity duality or various permutations
More informationAspects of integrability in classical and quantum field theories
Aspects of integrability in classical and quantum field theories Second year seminar Riccardo Conti Università degli Studi di Torino and INFN September 26, 2018 Plan of the talk PART 1 Supersymmetric 3D
More informationWilson loops and amplitudes in N=4 Super Yang-Mills
Wilson loops and amplitudes in N=4 Super Yang-Mills Vittorio Del Duca INFN LNF TH-LPCC CERN 8 August 2011 N=4 Super Yang-Mills maximal supersymmetric theory (without gravity) conformally invariant, β fn.
More informationAmplitudes & Wilson Loops at weak & strong coupling
Amplitudes & Wilson Loops at weak & strong coupling David Skinner - Perimeter Institute Caltech - 29 th March 2012 N=4 SYM, 35 years a!er Twistor space is CP 3, described by co-ords It carries a natural
More informationarxiv: v2 [hep-th] 23 Mar 2010
Y-system for Scattering Amplitudes Luis F. Alday a, Juan Maldacena a, Amit Sever b and Pedro Vieira b a School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA. alday,malda@ias.edu
More informationGauge/gravity duality: an overview. Z. Bajnok
Conference of the Middle European Cooperation in Statistical Physics, MECO37, March 18-22, 2012, Tatranské Matliare, Slovak Republik Gauge/gravity duality: an overview Z. Bajnok Theoretical Physics Research
More informationSeminar in Wigner Research Centre for Physics. Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013
Seminar in Wigner Research Centre for Physics Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013 Introduction - Old aspects of String theory - AdS/CFT and its Integrability String non-linear sigma
More informationA New Regulariation of N = 4 Super Yang-Mills Theory
A New Regulariation of N = 4 Super Yang-Mills Theory Humboldt Universität zu Berlin Institut für Physik 10.07.2009 F. Alday, J. Henn, J. Plefka and T. Schuster, arxiv:0908.0684 Outline 1 Motivation Why
More informationBremsstrahlung function for ABJM theory based on work in progress with L. Griguolo, M. Preti and D. Seminara
Bremsstrahlung function for ABJM theory based on work in progress with L. Griguolo, M. Preti and D. Seminara Lorenzo Bianchi Universität Hamburg March 3 rd,2017. YRISW, Dublin Lorenzo Bianchi (HH) Bremsstrahlung
More informationNumerical results in ABJM theory
Numerical results in ABJM theory Riccardo Conti Friday 3ʳᵈ March 2017 D. Bombardelli, A. Cavaglià, R. Conti and R. Tateo (in progress) Overview Purpose: Solving the Quantum Spectral Curve (QSC) equations
More informationFour-point functions in the AdS/CFT correspondence: Old and new facts. Emery Sokatchev
Four-point functions in the AdS/CFT correspondence: Old and new facts Emery Sokatchev Laboratoire d Annecy-le-Vieux de Physique Théorique LAPTH Annecy, France 1 I. The early AdS/CFT correspondence The
More informationScaling dimensions at small spin
Princeton Center for Theoretical Science Princeton University March 2, 2012 Great Lakes String Conference, Purdue University arxiv:1109.3154 Spectral problem and AdS/CFT correspondence Spectral problem
More informationSolving the AdS/CFT Y-system
Solving the AdS/CFT Y-system Dmytro Volin Nordita, Stockholm IHP, 2011 1110.0562 N.Gromov, V.Kazakov, S.Leurent. D.V. Setup: = IIB, AdS 5 xs 5 0 This is a talk about the spectral problem: Conformal dimension
More informationDuality between Wilson Loops and Scattering Amplitudes in QCD
Duality between Wilson Loops and Scattering Amplitudes in QCD by Yuri Makeenko (ITEP, Moscow) Based on: Y. M., Poul Olesen Phys. Rev. Lett. 12, 7162 (29) [arxiv:81.4778 [hep-th]] arxiv:93.4114 [hep-th]
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT Who? From? Where? When? Nina Miekley University of Würzburg Young Scientists Workshop 2017 July 17, 2017 (Figure by Stan Brodsky) Intuitive motivation What is meant by holography?
More informationBootstrapping the three-loop hexagon
CERN PH TH/2011/189 SLAC PUB 14528 LAPTH-029/11 HU-EP-11-38 NSF-KITP-11-176 Bootstrapping the three-loop hexagon Lance J. Dixon (1,2), James M. Drummond (1,3) and Johannes M. Henn (4,5) (1) PH-TH Division,
More informationTHE. Secret Life OF SCATTERING AMPLITUDES. based on work with Lionel Mason and with Mat Bullimore. David Skinner - Perimeter Institute
THE Secret Life OF SCATTERING AMPLITUDES based on work with Lionel Mason and with Mat Bullimore David Skinner - Perimeter Institute Kavli IPMU - 21 st May 2012 { Scattering amplitudes are quantum mechanical
More informationString/gauge theory duality and QCD
String/gauge theory duality and QCD M. Kruczenski Purdue University ASU 009 Summary Introduction String theory Gauge/string theory duality. AdS/CFT correspondence. Mesons in AdS/CFT Chiral symmetry breaking
More informationTowards a holographic formulation of cosmology
Towards a holographic formulation of cosmology Gonzalo Torroba Stanford University Topics in holography, supersymmetry and higher derivatives Mitchell Institute, Texas A&M, April 2013 During the last century,
More informationHolographic Entanglement and Interaction
Holographic Entanglement and Interaction Shigenori Seki RINS, Hanyang University and Institut des Hautes Études Scientifiques Intrication holographique et interaction à l IHES le 30 janvier 2014 1 Contents
More informationClassical AdS String Dynamics. In collaboration with Ines Aniceto, Kewang Jin
Classical AdS String Dynamics In collaboration with Ines Aniceto, Kewang Jin Outline The polygon problem Classical string solutions: spiky strings Spikes as sinh-gordon solitons AdS string ti as a σ-model
More informationDifference Painlevé equations from 5D gauge theories
Difference Painlevé equations from 5D gauge theories M. Bershtein based on joint paper with P. Gavrylenko and A. Marshakov arxiv:.006, to appear in JHEP February 08 M. Bershtein Difference Painlevé based
More informationSome analytic results from conformal bootstrap
25 June, 2015 Some analytic results from conformal bootstrap Aninda Sinha Indian Institute of Science, Bangalore Strings 2015, ICTS, Bangalore Strings 2015, ICTS, Bangalore Since the seminal work of Rattazzi,
More informationRECENT DEVELOPMENTS IN STRING THEORY International Conference Ascona, July Quantum spectral curve of N=4 SYM and its BFKL limit
RECENT DEVELOPMENTS IN STRING THEORY International Conference Ascona, 21 25 July 2014 Quantum spectral curve of N=4 SYM and its BFKL limit Vladimir Kazakov (ENS, Paris) Collaborations with: Nikolay Gromov
More informationIntroduction to Integrability in AdS/CFT: Lecture 4
Introduction to Integrability in AdS/CFT: Lecture 4 Rafael Nepomechie University of Miami Introduction Recall: 1-loop dilatation operator for all single-trace operators in N=4 SYM is integrable 1-loop
More informationarxiv: v3 [hep-th] 13 Jan 2012
Prepared for submission to JHEP arxiv:1109.6305v3 [hep-th] 13 Jan 2012 Deeper Look into Short Strings Nikolay Gromov a,b Saulius Valatka a a Mathematics Department, King s College London, The Strand, London
More informationNear BPS Wilson loop in AdS/CFT Correspondence
Near BPS Wilson loop in AdS/CFT Correspondence Chong-Sun Chu Durham University, UK Based on paper arxiv:0708.0797[hep-th] written in colaboration with Dimitrios Giataganas Talk given at National Chiao-Tung
More informationN = 4 SYM and new insights into
N = 4 SYM and new insights into QCD tree-level amplitudes N = 4 SUSY and QCD workshop LPTHE, Jussieu, Paris Dec 12, 2008 Henrik Johansson, UCLA Bern, Carrasco, HJ, Kosower arxiv:0705.1864 [hep-th] Bern,
More information1/N Expansions in String and Gauge Field Theories. Adi Armoni Swansea University
1/N Expansions in String and Gauge Field Theories Adi Armoni Swansea University Oberwoelz, September 2010 1 Motivation It is extremely difficult to carry out reliable calculations in the strongly coupled
More informationScaling and integrability from AdS 5 S 5
Scaling and integrability from AdS 5 S 5 Riccardo Ricci Imperial College London DAMTP Cambridge 14th October Work in collaboration with S. Giombi, R.Roiban, A. Tseytlin and C.Vergu Outline Introduction
More informationAccepted Manuscript. Temperature quantization from the TBA equations. Sergey Frolov, Ryo Suzuki
Accepted Manuscript Temperature quantization from the TBA equations Sergey Frolov, Ryo Suzuki PII: S0370-2693(09)00783-7 DOI: 10.1016/j.physletb.2009.06.069 Reference: PLB 25985 To appear in: Physics Letters
More informationRecent developments in Monte Carlo studies of superstring theory
Recent developments in Monte Carlo studies of superstring theory Jun Nishimura (KEK & SOKENDAI) 12-16 August, 2013 Current Themes in High Energy Physics and Cosmology Niels Bohr Institute, Copenhagen Large-N
More informationThe Steinmann Cluster Bootstrap for N = 4 SYM Amplitudes
The Steinmann Cluster Bootstrap for N = 4 SYM Amplitudes Georgios Papathanasiou 1412.3763 w/ Drummond,Spradlin 1612.08976 w/ Dixon,Drummond,Harrington,McLeod,Spradlin + in progress w/ Caron-Huot,Dixon,McLeod,von
More informationTHE SPECTRUM OF BOUNDARY SINE- GORDON THEORY
THE SPECTRUM OF BOUNDARY SINE- GORDON THEORY Z. Bajnok, L. Palla and G. Takács Institute for Theoretical Physics, Eötvös University, Budapest, Hungary Abstract We review our recent results on the on-shell
More informationChern-Simons Theories and AdS/CFT
Chern-Simons Theories and AdS/CFT Igor Klebanov PCTS and Department of Physics Talk at the AdS/CMT Mini-program KITP, July 2009 Introduction Recent progress has led to realization that coincident membranes
More informationNon-Planar N =4 SYM at Four Loops and Supersum Structures
Non-Planar N =4 SYM at Four Loops and Supersum Structures NBIA workshop Aug 12, 2009 Henrik Johansson UCLA & IPhT Saclay 0903.5348[hep-th]: Z.Bern, J.J.Carrasco, H.Ita, HJ, R.Roiban to appear: Z.Bern,
More informationIntegrability from Emergent Gauge Theory
Integrability from Emergent Gauge Theory (Based on work with JiaHui Huang, Minkyoo Kim, Laila Tribelhorn and Jaco Van Zyl) Robert de Mello Koch South China Normal University and Mandelstam Institute for
More informationCFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space
CFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space Igor Klebanov Talk at New England Strings Meeting Brown University November 6, 2015 Based mainly on L. Fei, S. Giombi, IK, arxiv:1404.1094
More informationHolographic methods for cosmology. Gonzalo Torroba Stanford University
Holographic methods for cosmology Gonzalo Torroba Stanford University Observations and Theoretical Challenges in Primordial Cosmology KITP, UCSB, April 2013 Members of the collaboration Matt Dodelson Shunji
More informationContinuum limit of fishnet graphs and AdS sigma model
Continuum limit of fishnet graphs and AdS sigma model Benjamin Basso LPTENS 15th Workshop on Non-Perturbative QCD, IAP, Paris, June 2018 based on work done in collaboration with De-liang Zhong Motivation
More informationHalf BPS solutions in type IIB and M-theory
Half BPS solutions in type IIB and M-theory Based on work done in collaboration with Eric D Hoker, John Estes, Darya Krym (UCLA) and Paul Sorba (Annecy) E.D'Hoker, J.Estes and M.G., Exact half-bps type
More informationAntenna on Null Polygon ABJM Wilson Loop
Antenna on Null Polygon ABJM Wilson Loop Soo-Jong Rey Seoul National University, Seoul KOREA Institute of Basic Sciences, Daejeon KOREA Scattering Amplitudes at Hong Kong IAS November 21, 2014 Soo-Jong
More informationAdS/CFT Correspondence and Entanglement Entropy
AdS/CFT Correspondence and Entanglement Entropy Tadashi Takayanagi (Kyoto U.) Based on hep-th/0603001 [Phys.Rev.Lett.96(2006)181602] hep-th/0605073 [JHEP 0608(2006)045] with Shinsei Ryu (KITP) hep-th/0608213
More informationEvolution of 3D-PDFs at Large-x B and Generalized Loop Space
Evolution of 3D-PDFs at Large-x B and Generalized Loop Space Igor O. Cherednikov Universiteit Antwerpen QCD Evolution Workshop Santa Fe (NM), 12-16 May 2014 What we can learn from the study of Wilson loops?
More informationPerturbative Integrability of large Matrix Theories
35 th summer institute @ ENS Perturbative Integrability of large Matrix Theories August 9 th, 2005 Thomas Klose Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Potsdam, Germany
More informationKentaroh Yoshida (Kyoto Univ.)
2014/03/04 ``Progress in the synthesis of integrabilities arising from gauge string duality Recent progress on q deformations of the AdS 5 5 x S superstring Kentaroh Yoshida (Kyoto Univ.) In collaboration
More informationY-system for the exact spectrum of N = 4 SYM
Universitȁt von Bonn, 6 Juni 2011 Y-system for the exact spectrum of N = 4 SYM Vladimir Kazakov (ENS,Paris) Theoretical Challenges in Quantum Gauge Field Theory QFT s in dimension>2, in particular 4D Yang-Mills
More informationM-theory S-Matrix from 3d SCFT
M-theory S-Matrix from 3d SCFT Silviu S. Pufu, Princeton University Based on: arxiv:1711.07343 with N. Agmon and S. Chester arxiv:1804.00949 with S. Chester and X. Yin Also: arxiv:1406.4814, arxiv:1412.0334
More informationLarge spin systematics in CFT
University of Oxford Holography, Strings and Higher Spins at Swansea with A. Bissi and T. Lukowski Introduction The problem In this talk we will consider operators with higher spin: T rϕ µ1 µl ϕ, T rϕϕ
More informationTwistors, amplitudes and gravity
Twistors, amplitudes and gravity From twistor strings to quantum gravity? L.J.Mason The Mathematical Institute, Oxford lmason@maths.ox.ac.uk LQG, Zakopane 4/3/2010 Based on JHEP10(2005)009 (hep-th/0507269),
More informationAnalytic bootstrap at large spin
Analytic bootstrap at large spin Aninda Sinha Indian Institute of Science, Bangalore Work done with Apratim Kaviraj, Kallol Sen arxiv:1502.0143 and to appear soon. Summary of main results Given a (4d for
More informationAdS 6 /CFT 5 in Type IIB
AdS 6 /CFT 5 in Type IIB Part II: Dualities, tests and applications Christoph Uhlemann UCLA Strings, Branes and Gauge Theories APCTP, July 2018 arxiv: 1606.01254, 1611.09411, 1703.08186, 1705.01561, 1706.00433,
More informationGökçe Başar. University of Maryland. July 25, Resurgence in Gauge and String Theories, Lisboa, 2016
Resurgence, exact WKB and quantum geometry Gökçe Başar University of Maryland July 25, 2016 Resurgence in Gauge and String Theories, Lisboa, 2016 based on: 1501.05671 with G.Dunne, 16xx.xxxx with G.Dunne,
More informationA New Identity for Gauge Theory Amplitudes
A New Identity for Gauge Theory Amplitudes Hidden Structures workshop, NBI Sept 10, 2008 Henrik Johansson, UCLA Z. Bern, J.J. Carrasco, HJ arxive:0805 :0805.3993 [hep-ph[ hep-ph] Z. Bern, J.J. Carrasco,
More informationAdS/CFT Beyond the Planar Limit
AdS/CFT Beyond the Planar Limit T.W. Brown Queen Mary, University of London Durham, October 2008 Diagonal multi-matrix correlators and BPS operators in N=4 SYM (0711.0176 [hep-th]) TWB, Paul Heslop and
More information