Counting BPS states in E#string theory. Kazuhiro Sakai
|
|
- Stephanie Allison
- 6 years ago
- Views:
Transcription
1 Progress in Quantum Field Theory and String Theory Osaka City University, 06 April 2012 Counting BPS states in E#string theory Kazuhiro Sakai!YITP, Kyoto University" arxiv: arxiv:
2 String theory predicts the existence of nontrivial QFTs in 6D. The worldvolume theory of multiple M5 branes ### (2,0) SUSY!16 supercharges" What about theories with (1,0) SUSY? Heterotic string theories on K3!16 8 supercharges" What happens when instantons in K3 shrink to zero size? Small SO(32) instantons extra Sp(n) gauge symmetry worldvolume theory of n type I D5#branes What about small E8 instantons?!witten 95"
3 M#theory description of the E 8 E 8 heterotic string theory on K3 9-brane M5-brane 9-brane M2-brane x 0 x 5 E-string a zero#size E 8 #instanton x 11 K3 x 6 x 9
4 E#string theory!ganor#hanany 96"!Seiberg#Witten 96" 6D (1,0)#supersymmetric local QFT decoupled from gravity no vector multiplets Coulomb branch ### a tensor multiplet Higgs branch = the moduli space of an E8 instanton fundamental excitations ### strings global E8 symmetry E#string = 1 heterotic E 2 8 E 8 string
5 Toroidal compactification down to 4D a 4D N = 2 theory described by Seiberg#Witten theory SU(n) gauge theories E#string theory Seiberg#Witten curves are known realized by String Theory on certain CY3 Lagrangian description toric CY3 no Lagrangian description non#toric CY3 Nekrasov partition functions are known Any analogue? Yes!!at least partly"
6 Heterotic ## F#theory duality!morrison#vafa 96" Heterotic on K3 E#strings on R 6 F#theory on CY3 E#strings on R 6 M#theory on CY3 E#strings on R 5 S 1 = 1 2 local K3 surface!the total space of the canonical bundle of a K3 surface" local 2K3!non#compact CY3" 1 2 K3
7 Partition function of BPS wound E#strings! = prepotential" F 0 (ϕ, τ )= n=1 k=0 N n,k m=1 p mn q mk m 3 p := e 2πiϕ, q := e 2πiτ n : winding number k : momentum N n,k : BPS multiplicity!instanton number"!klemm#mayr#vafa 96" k n
8 Winding number expansion F 0 (ϕ, τ )= n=1 Q n Z n (τ ) Q := q 1/2 p, p := e 2πiϕ, q := e 2πiτ 1 Z n : partition function of N = 4 U(n) topological SYM on 2K3 Z 1 = E 4 η 12, Z 2 = E 2E E 4E 6 24η 24, Z n = P 6n 2(E 2,E 4,E 6 ) η 12n!Minahan#Nemeschansky#Vafa#Warner 98" E 2n (τ ) : Eisenstein series η(τ ) : Dedekind eta function
9 The expansion coe$cients Zn at low orders can be computed either from the Seiberg#Witten curve or from!minahan#nemeschansky#warner 97" y 2 =4x E 4(τ )u 4 x E 6(τ )u 6 +4u 5 the modular anomaly equation E2 Z n = 1 24 and the gap condition n 1 k=1 k(n k)z k Z n k q n/2 Z n = 1 n 3 + O(qn )
10 Nekrasov#type expression for the prepotential!k.s. 12" F 0 = (2 2 ln Z) =0 Z = R Q R a,b,c,d (i,j) R ab ϑ ab ( 1 2π (j i), τ ) 2 ϑ 1 a c,1 b d ( 1 2π h ab,cd(i, j), τ ) 2 R =(R 11,R 10,R 00,R 01 ) a, b, c, d =0, 1 Rab : partition µ ab,2 µ ab,1 ϑ ab (z, τ ) : Jacobi theta functions h ab,cd (i, j) := µ ab,i + µ cd,j i j +1!relative hook#length" i j Rcd Rab
11 The expression coincides with a special case of!k.s. 12" the elliptic generalization of the Nekrasov partition function for SU(4) SYM with Nf = 8 massless fundamental hypermultiplets!nekrasov 02"!Hollowood#Iqbal#Vafa 03" Z = R ( p) R 4 k=1 (i,j) R k ( ϑ 1 ak + 1 2π (j i), τ ) 8 4 l=1 ϑ ( 1 ak a l + 1 2π h kl(i, j), τ ) 2 a 1 =0, a 2 = 1 2, a 3 = 1+τ 2, a 4 = τ 2 R =(R 1,R 2,R 3,R 4 )=(R 11,R 10,R 00,R 01 )
12 The prepotential represents g = 0 topological string amplitude F 0 = F 1 2 K3 0 However, Z = Z 1 2 K3 ( ) := exp g=0 2g 2 F 1 2 K3 g Di%erence of modular anomalies E2 Z = φ Z E2 Z 1 2 K3 = φ ( φ + 1)Z 1 2 K3!Hosono#Saito#Takahashi 99" E2 F 0 = 1 24 ( φf 0 ) 2 φ = 1 2πi ϕ = Q Q
13 Part II 1 Topological string amplitudes for the most general local 2K3
14 Topological string amplitudes at higher genus Holomorphic anomaly equation!bershadsky#cecotti#ooguri#vafa 93" īf g = 1 ( ) g 1 2 Cī j ke 2K G j j G k k D j D k F g 1 + D j F h D k F g h Recent developments F g are quasi#automorphic forms!aganagic#bouchard#klemm 06" For SU(2) gauge theories: F g are polynomials in h=1 F g are polynomials in a finite number of generators Ẽ 2 := E 2 ( τ ) Direct integration method!grimm#klemm#mariño#weiss 06" HAE: Ẽ2 F g =!Yamaguchi#Yau 04"!Alim#Länge 07"
15 1 Topological string amplitudes for the most general local K3 Z 1 2 K3 (ϕ, τ, µ; ) = exp [ g=0 2g 2 n=1 For low g and n, Zg,n can be determined by symmetry T g,n (τ, µ) : Z g,n (τ, µ) = holomorphic anomaly equation eπinτ η(τ ) 12n T g,n(τ, µ) E2 Z 1 2 K3 = φ ( φ + 1)Z 1 2 K3 2 e 2πinϕ Z g,n (τ, µ) W (E 8 )#invariant quasi#jacobi form of weight 2g 2+6n and index gap condition No BPS states for k < n!except for n =1"!Minahan#Nemeschansky#Vafa#Warner 98"!Hosono#Saito#Takahashi 99" n ]
16 Seiberg#Witten curve for the E#string theory!eguchi#k.s. 02" y 2 =4x 3 fx g f = 4 a n u 4 n, g = 6 b n u 6 n. n=0 n=0 a n (τ, µ), b n (τ, µ) are expressed in terms of W (E 8 )#invariant Jacobi forms A n (τ, µ), B n (τ, µ) a 0 = 1 12 E 4, a 1 =0, a 2 = 6 ( ) E 4 A 2 + A 2 1, E 4 b 0 = E 6, b 1 = 4 E 4 A 1, b 2 = 5 6E 2 4 ( E 2 4 B 2 E 6 A 2 1 ),
17 W (E 8 )#invariant Jacobi forms!k.s. 11" Θ(τ, µ) = ϑ k (µ j, τ ) k=1 j=1 Theta function associated with the E 8 root lattice A 2 (τ, µ) = 8 H {Θ(2τ, 2 µ)}, 9 A 1(τ, µ) =Θ(τ, µ), A 3 (τ, µ) = H {Θ(3τ, 3 µ)}, A 4(τ, µ) =Θ(τ, 2 µ), A 5 (τ, µ) = 125 H {Θ(5τ, 5 µ)}, 126 B 2 (τ, µ) = 32 5 H {e 1(τ )Θ(2τ, 2 µ)}, B 3 (τ, µ) = H { h(τ ) 2 Θ(3τ, 3 µ) }, B 4 (τ, µ) = H { ϑ 4 (2τ ) 4 Θ(4τ, 4 µ) }, B 6 (τ, µ) = 9 10 H { h(τ ) 2 Θ(6τ, 6 µ) }. H { } : sum of all possible SL(2, Z) transforms e 1 (τ )= 1 12 ( ϑ3 (τ ) 4 + ϑ 4 (τ ) 4), A n (τ, 0) = E 4, h(τ )=ϑ 3 (2τ )ϑ 3 (6τ )+ϑ 2 (2τ )ϑ 2 (6τ ). B n (τ, 0) = E 6.
18 F 0 = 2 φ t, F 1 = 1 2 ln ω 1 12 ln ln 1 2 φ, F 2 = 1 96 E Ẽ2 φ ln ω Ẽ2( φ ln ω) (Ẽ2 2 Ẽ 4 ) φ t φ ln ω F 3 = t := 2πi( τ τ ) Ẽ 2n := E 2n ( τ ) := η( τ ) 24!K.S. 11" (5Ẽ2 2 +3Ẽ 4 ) 2 φ t (35Ẽ Ẽ 4 Ẽ 2 86Ẽ 6 )( φ t) 2, Structure of F g (g 2) 1 2 Amplitudes for the local K3 2πω τ 0 2πω polynomial in Ẽ 2k, m φ ln ω, n φ t each term contains 2g 2 φ s quasi-modular form of weight 2g 2 ([Ẽ 2k ]=2k, [ mφ ln ω] =0, [ nφ t]= 2 )
19 Summary We have found a Nekrasov#type expression for the Seiberg#Witten prepotential for the E#string theory. We have constructed topological string amplitudes 1 for the most general local K3!up to genus three". 2
20 SU(2) Seiberg#Witten theories with various flavor symmetries Seiberg#Witten curves ### constructed for all theories!seiberg#witten 94"!Minahan#Nemeschansky 96"!Ganor#Morrison#Seiberg 96"!Minahan#Nemeschansky#Warner 97"!Eguchi#K.S. 02" All#genus partition functions: 6D The Ê 8 #string theory needs further investigation! 5D E 8 E 7 E 6 E 5 E 4 E 3 E 2 E 1 E 0 Ẽ 1 4D E 8 E 7 E 6 D 4!Minahan#Nemeschansky 96" D 3 D 2 D 1 D 0 Partition functions were constructed E 9 = Êby 8 the ruled vertex formalism!diaconescu#florea 05" A 2 A 1 A 0!Argyres#Plesser#Seiberg#Witten 95" Nekrasov partition functions are available for these theories!nekrasov 02"
Microstates of AdS black holes and supersymmetric localization
Microstates of AdS black holes and supersymmetric localization Seyed Morteza Hosseini Università di Milano-Bicocca IPM, Tehran, May 8-11, 2017 Recent Trends in String Theory and Related Topics in collaboration
More informationWhat is F-theory? David R. Morrison. University of California, Santa Barbara
University of California, Santa Barbara Physics and Geometry of F-theory 2015 Max Plack Institute for Physics, Munich 25 February 2015 arxiv:1503.nnnnn Inspired in part by Grassi Halverson Shaneson arxiv:1306.1832
More informationInstantons and Donaldson invariants
Instantons and Donaldson invariants George Korpas Trinity College Dublin IFT, November 20, 2015 A problem in mathematics A problem in mathematics Important probem: classify d-manifolds up to diffeomorphisms.
More informationInstanton effective action in - background and D3/D(-1)-brane system in R-R background
Instanton effective action in - background and D3/D(-1)-brane system in R-R background Speaker : Takuya Saka (Tokyo Tech.) Collaboration with Katsushi Ito, Shin Sasaki (Tokyo Tech.) And Hiroaki Nakajima
More informationTriality of Two-dimensional (0,2) Theories
J.Guo,B.Jia,E.Sharpe,arXiv:1501.00987 April 11, 2015 Outline 1 2d N = (0,2) Gauge Theories 2 Triality Proposal Checks Low Energy Description 3 Chiral Rings Chiral Rings in (0,2) Theories Bott-Borel-Weil
More informationTHE MASTER SPACE OF N=1 GAUGE THEORIES
THE MASTER SPACE OF N=1 GAUGE THEORIES Alberto Zaffaroni CAQCD 2008 Butti, Forcella, Zaffaroni hepth/0611229 Forcella, Hanany, Zaffaroni hepth/0701236 Butti,Forcella,Hanany,Vegh, Zaffaroni, arxiv 0705.2771
More informationDyon degeneracies from Mathieu moonshine
Prepared for submission to JHEP Dyon degeneracies from Mathieu moonshine arxiv:1704.00434v2 [hep-th] 15 Jun 2017 Aradhita Chattopadhyaya, Justin R. David Centre for High Energy Physics, Indian Institute
More informationLittle strings and T-duality
Little strings and T-duality Jungmin Kim (Seoul National University) January 28, 2015 Talk based on [JK., Seok Kim, Kimyeong Lee] in progress. 6d N=(1,1) Little strings Outline NS5-branes in IIB string
More informationString Theory in a Nutshell. Elias Kiritsis
String Theory in a Nutshell Elias Kiritsis P R I N C E T O N U N I V E R S I T Y P R E S S P R I N C E T O N A N D O X F O R D Contents Preface Abbreviations xv xvii Introduction 1 1.1 Prehistory 1 1.2
More informationDualities and Topological Strings
Dualities and Topological Strings Strings 2006, Beijing - RD, C. Vafa, E.Verlinde, hep-th/0602087 - work in progress w/ C. Vafa & C. Beasley, L. Hollands Robbert Dijkgraaf University of Amsterdam Topological
More informationLecture 24 Seiberg Witten Theory III
Lecture 24 Seiberg Witten Theory III Outline This is the third of three lectures on the exact Seiberg-Witten solution of N = 2 SUSY theory. The third lecture: The Seiberg-Witten Curve: the elliptic curve
More informationLecture 7: N = 2 supersymmetric gauge theory
Lecture 7: N = 2 supersymmetric gauge theory José D. Edelstein University of Santiago de Compostela SUPERSYMMETRY Santiago de Compostela, November 22, 2012 José D. Edelstein (USC) Lecture 7: N = 2 supersymmetric
More informationSuperconformal Partition Functions and Non-perturbative Topological Strings
Superconformal Partition Functions and Non-perturbative Topological Strings arxiv:1210.5909v3 [hep-th] 23 Apr 2013 Guglielmo Lockhart and Cumrun Vafa Jefferson Physical Laboratory, Harvard University,
More informationAspects of (0,2) theories
Aspects of (0,2) theories Ilarion V. Melnikov Harvard University FRG workshop at Brandeis, March 6, 2015 1 / 22 A progress report on d=2 QFT with (0,2) supersymmetry Gross, Harvey, Martinec & Rohm, Heterotic
More information5d SCFTs and instanton partition functions
5d SCFTs and instanton partition functions Hirotaka Hayashi (IFT UAM-CSIC) Hee-Cheol Kim and Takahiro Nishinaka [arxiv:1310.3854] Gianluca Zoccarato [arxiv:1409.0571] Yuji Tachikawa and Kazuya Yonekura
More informationS-CONFINING DUALITIES
DIMENSIONAL REDUCTION of S-CONFINING DUALITIES Cornell University work in progress, in collaboration with C. Csaki, Y. Shirman, F. Tanedo and J. Terning. 1 46 3D Yang-Mills A. M. Polyakov, Quark Confinement
More informationTopological reduction of supersymmetric gauge theories and S-duality
Topological reduction of supersymmetric gauge theories and S-duality Anton Kapustin California Institute of Technology Topological reduction of supersymmetric gauge theories and S-duality p. 1/2 Outline
More informationarxiv: v2 [hep-th] 12 Apr 2016
Prepared for submission to JHEP S-duality, triangle groups and modular anomalies in = SQCD arxiv:1601.0187v [hep-th] 1 Apr 016 S. K. Ashok, a E. Dell Aquila, a A. Lerda b and M. Raman a a Institute of
More informationTechniques for exact calculations in 4D SUSY gauge theories
Techniques for exact calculations in 4D SUSY gauge theories Takuya Okuda University of Tokyo, Komaba 6th Asian Winter School on Strings, Particles and Cosmology 1 First lecture Motivations for studying
More informationA Localization Computation in Confining Phase
A Localization Computation in Confining Phase Seiji Terashima (YITP) 20 January 2015 at Osaka based on the paper: arxiv:1410.3630 Introduction 2 Analytic computations in QFT are hopeless, but, some exceptions:
More informationN = 2 heterotic string compactifications on orbifolds of K3 T 2
Prepared for submission to JHEP N = 2 heterotic string compactifications on orbifolds of K3 T 2 arxiv:6.0893v [hep-th 7 Nov 206 Aradhita Chattopadhyaya, Justin R. David Centre for High Energy Physics,
More informationNon-Supersymmetric Seiberg duality Beyond the Planar Limit
Non-Supersymmetric Seiberg duality Beyond the Planar Limit Input from non-critical string theory, IAP Large N@Swansea, July 2009 A. Armoni, D.I., G. Moraitis and V. Niarchos, arxiv:0801.0762 Introduction
More informationThree-Charge Black Holes and ¼ BPS States in Little String Theory
Three-Charge Black Holes and ¼ BPS States in Little String Theory SUNGJAY LEE KOREA INSTITUTE FOR ADVANCED STUDIES Joint work (JHEP 1512, 145) with Amit Giveon, Jeff Harvey, David Kutasov East Asia Joint
More informationA Landscape of Field Theories
A Landscape of Field Theories Travis Maxfield Enrico Fermi Institute, University of Chicago October 30, 2015 Based on arxiv: 1511.xxxxx w/ D. Robbins and S. Sethi Summary Despite the recent proliferation
More information4d N=2 as 6d N=(2,0) compactified on C
Yesterday Basics of 6d N=(2,0) theory. S-duality of 4d N=4. Today 4d N=2 as 6d N=(2,0) compactified on C Tomorrow Relation with 2d CFT Yesterday s talk s summary 6d N=(2,0) theory comes in types G= A,D,E
More informationQuantum Black Holes, Localization & Mock Modular Forms
Quantum Black Holes, Localization & Mock Modular Forms ATISH DABHOLKAR CNRS University of Paris VI VII Regional Meeting in String Theory 19 June 2013, Koλυµπαρι Atish Dabholkar (Paris) Quantum Black Holes
More informationF-Theory, Spinning Black Holes and Multi-string Branches
F-Theory, Spinning Black Holes and Multi-string Branches arxiv:1509.00455v3 [hep-th] 2 Dec 2015 Babak Haghighat 1,2, Sameer Murthy 3, Cumrun Vafa 1, Stefan Vandoren 4 1 Jefferson Physical Laboratory, Harvard
More informationRigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1
Rigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1 Ofer Aharony Weizmann Institute of Science 8 th Crete Regional Meeting on String Theory, Nafplion, July 9, 2015 OA, Berkooz, Rey, 1501.02904 Outline
More informationThree-Charge Black Holes and ¼ BPS States in Little String Theory I
Three-Charge Black Holes and ¼ BPS States in Little String Theory I SUNGJAY LEE KOREA INSTITUTE FOR ADVANCED STUDIES UNIVERSITY OF CHICAGO Joint work (1508.04437) with Amit Giveon, Jeff Harvey, David Kutasov
More informationLoop Amplitudes from Ambitwistor Strings
Loop Amplitudes from Ambitwistor Strings Yvonne Geyer QCD meets Gravity Workshop Dec 5-9, 2016 UCLA arxiv:1507.00321, 1511.06315, 1607.08887 YG, L. Mason, R. Monteiro, P. Tourkine Motivation: worldsheet
More informationSupermatrix Models * Robbert Dijkgraaf Ins$tute for Advanced Study
Supermatrix Models * Robbert Dijkgraaf Ins$tute for Advanced Study Walter Burke Ins.tute for Theore.cal Physics Inaugural Symposium Caltech, Feb 24, 1015 * Work with Cumrun Vafa and Ben Heidenreich, in
More informationBlack Hole Microstate Counting using Pure D-brane Systems
Black Hole Microstate Counting using Pure D-brane Systems HRI, Allahabad, India 11.19.2015 UC Davis, Davis based on JHEP10(2014)186 [arxiv:1405.0412] and upcoming paper with Abhishek Chowdhury, Richard
More informationQuantum Black Holes, Localization & Mock Modular Forms
Quantum Black Holes, Localization & Mock Modular Forms ATISH DABHOLKAR CERN, GENEVA CNRS/ UNIVERSITY OF PARIS VI Geometry and Physics ASI Workshop Munich 22 November 2012 Atish Dabholkar (CERN/Paris) Quantum
More informationSolution Set 8 Worldsheet perspective on CY compactification
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics String Theory (8.821) Prof. J. McGreevy Fall 2007 Solution Set 8 Worldsheet perspective on CY compactification Due: Monday, December 18, 2007
More informationSupersymmetric Gauge Theories, Matrix Models and Geometric Transitions
Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions Frank FERRARI Université Libre de Bruxelles and International Solvay Institutes XVth Oporto meeting on Geometry, Topology and Physics:
More informationCOUNTING BPS STATES IN CONFORMAL GAUGE THEORIES
COUNTING BPS STATES IN CONFORMAL GAUGE THEORIES Alberto Zaffaroni PISA, MiniWorkshop 2007 Butti, Forcella, Zaffaroni hepth/0611229 Forcella, Hanany, Zaffaroni hepth/0701236 Butti,Forcella,Hanany,Vegh,
More information2 Type IIA String Theory with Background Fluxes in d=2
2 Type IIA String Theory with Background Fluxes in d=2 We consider compactifications of type IIA string theory on Calabi-Yau fourfolds. Consistency of a generic compactification requires switching on a
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationarxiv: v2 [hep-th] 24 May 2012
IPMU 12-0093 arxiv:1205.3652v2 [hep-th] 24 May 2012 On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit Min-xin Huang Kavli Institute for the Physics and Mathematics of the Universe (Kavli
More informationString Phenomenology ???
String Phenomenology Andre Lukas Oxford, Theoretical Physics d=11 SUGRA IIB M IIA??? I E x E 8 8 SO(32) Outline A (very) basic introduction to string theory String theory and the real world? Recent work
More informationSymmetries Then and Now
Symmetries Then and Now Nathan Seiberg, IAS 40 th Anniversary conference Laboratoire de Physique Théorique Global symmetries are useful If unbroken Multiplets Selection rules If broken Goldstone bosons
More informationRefined Chern-Simons Theory, Topological Strings and Knot Homology
Refined Chern-Simons Theory, Topological Strings and Knot Homology Based on work with Shamil Shakirov, and followup work with Kevin Scheaffer arxiv: 1105.5117 arxiv: 1202.4456 Chern-Simons theory played
More information1 Electrons on a lattice, with noisy electric field
IHES-P/05/34 XXIII Solvay Conference Mathematical structures: On string theory applications in condensed matter physics. Topological strings and two dimensional electrons Prepared comment by Nikita Nekrasov
More informationOne-loop corrections to heterotic flux compactifications,
One-loop corrections to heterotic flux compactifications Dan Israël Imperial College, May 14th 2016 New supersymmetric index of heterotic compactifications with torsion, D.I. and Matthieu Sarkis, JHEP
More informationElliptic Genera of non-compact CFTs
Elliptic Genera of non-compact CFTs Sujay K. Ashok IMSc, Chennai (work done with Jan Troost) Indian Strings Meeting, December 2012 arxiv:1101.1059 [hep-th] arxiv:1204.3802 [hep-th] arxiv:1212.xxxx [hep-th]
More informationSphere Partition Functions, Topology, the Zamolodchikov Metric
Sphere Partition Functions, Topology, the Zamolodchikov Metric, and Extremal Correlators Weizmann Institute of Science Efrat Gerchkovitz, Jaume Gomis, ZK [1405.7271] Jaume Gomis, Po-Shen Hsin, ZK, Adam
More informationN = 2 supersymmetric gauge theory and Mock theta functions
N = 2 supersymmetric gauge theory and Mock theta functions Andreas Malmendier GTP Seminar (joint work with Ken Ono) November 7, 2008 q-series in differential topology Theorem (M-Ono) The following q-series
More informationDualities and 5-Brane Webs for 5d rank 2 SCFTs
Dualities and 5-Brane Webs for 5d rank 2 SCFTs Kimyeong Lee Korea Institute for Advanced Study Hirotaka Hayashi (Tokai Univ), Sung-Soo Kim (UESTC), Futoshi Yagi (Technion) [arxiv:1801.03916] and [arxiv:1806.10569]
More informationHeterotic Torsional Backgrounds, from Supergravity to CFT
Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,
More informationNovel potentials for string axion inflation
Novel potentials for string axion inflation 1. Introduction Tatsuo Kobayashi. Threshold corrections: Dedekind eta function 3. Quantum corrected period vector 4. Summary Abe, T.K., Otsuka, arxiv:1411.4768
More informationInstantons in string theory via F-theory
Instantons in string theory via F-theory Andrés Collinucci ASC, LMU, Munich Padova, May 12, 2010 arxiv:1002.1894 in collaboration with R. Blumenhagen and B. Jurke Outline 1. Intro: From string theory to
More informationLecture 8: 1-loop closed string vacuum amplitude
Lecture 8: 1-loop closed string vacuum amplitude José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 5, 2013 José D. Edelstein (USC) Lecture 8: 1-loop vacuum
More informationDirect integration for general Ω backgrounds
ATMP-6-3-A-HUA 03// 9:34 page 805 # c 0 International Press Adv. Theor. Math. Phys. 6 (0) 805 849 Direct integration for general Ω backgrounds Min-xin Huang and Albrecht Klemm Institute for the Physics
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 information2D CFTs for a class of 4D N = 1 theories
2D CFTs for a class of 4D N = 1 theories Vladimir Mitev PRISMA Cluster of Excellence, Institut für Physik, THEP, Johannes Gutenberg Universität Mainz IGST Paris, July 18 2017 [V. Mitev, E. Pomoni, arxiv:1703.00736]
More informationA Review of Solitons in Gauge Theories. David Tong
A Review of Solitons in Gauge Theories David Tong Introduction to Solitons Solitons are particle-like excitations in field theories Their existence often follows from general considerations of topology
More informationFree fermion and wall-crossing
Free fermion and wall-crossing Jie Yang School of Mathematical Sciences, Capital Normal University yangjie@cnu.edu.cn March 4, 202 Motivation For string theorists It is called BPS states counting which
More informationHow to resum perturbative series in supersymmetric gauge theories. Masazumi Honda ( 本多正純 )
How to resum perturbative series in supersymmetric gauge theories Masazumi Honda ( 本多正純 ) References: M.H., Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories, PRL116,
More informationGeneralized Kac-Moody Algebras from CHL Dyons
Generalized Kac-Moody Algebras from CHL Dyons Suresh Govindarajan Department of Physics Indian Institute of Technology Madras Talk at CHEP on Sept. 9, 2008 Based on arxiv:0807.4451 with K. Gopala Krishna
More informationAmbitwistor Strings beyond Tree-level Worldsheet Models of QFTs
Ambitwistor Strings beyond Tree-level Worldsheet Models of QFTs Yvonne Geyer Strings 2017 Tel Aviv, Israel arxiv:1507.00321, 1511.06315, 1607.08887 YG, L. Mason, R. Monteiro, P. Tourkine arxiv:170x.xxxx
More informationFactorization Algebras Associated to the (2, 0) Theory IV. Kevin Costello Notes by Qiaochu Yuan
Factorization Algebras Associated to the (2, 0) Theory IV Kevin Costello Notes by Qiaochu Yuan December 12, 2014 Last time we saw that 5d N = 2 SYM has a twist that looks like which has a further A-twist
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationTopological String Theory
Topological String Theory Hirosi Ooguri (Caltech) Strings 2005, Toronto, Canada If String Theory is an answer, what is the question? What is String Theory? If Topological String Theory is an answer, what
More informationThe Affleck Dine Seiberg superpotential
The Affleck Dine Seiberg superpotential SUSY QCD Symmetry SUN) with F flavors where F < N SUN) SUF ) SUF ) U1) U1) R Φ, Q 1 1 F N F Φ, Q 1-1 F N F Recall that the auxiliary D a fields: D a = gφ jn T a
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT D-branes Type IIA string theory: Dp-branes p even (0,2,4,6,8) Type IIB string theory: Dp-branes p odd (1,3,5,7,9) 10D Type IIB two parallel D3-branes low-energy effective description:
More informationExact Results in D=2 Supersymmetric Gauge Theories And Applications
Exact Results in D=2 Supersymmetric Gauge Theories And Applications Jaume Gomis Miami 2012 Conference arxiv:1206.2606 with Doroud, Le Floch and Lee arxiv:1210.6022 with Lee N = (2, 2) supersymmetry on
More informationTwo Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges. Adi Armoni Swansea University
Two Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges Adi Armoni Swansea University Queen Mary, April 2009 1 Introduction Seiberg duality (Seiberg 1994) is a highly non-trivial
More informationPossible Advanced Topics Course
Preprint typeset in JHEP style - HYPER VERSION Possible Advanced Topics Course Gregory W. Moore Abstract: Potential List of Topics for an Advanced Topics version of Physics 695, Fall 2013 September 2,
More informationFixing all moduli in F-theory and type II strings
Fixing all moduli in F-theory and type II strings 0504058 Per Berglund, P.M. [0501139 D. Lüst, P.M., S. Reffert, S. Stieberger] 1 - Flux compactifications are important in many constructions of string
More informationGauge Threshold Corrections for Local String Models
Gauge Threshold Corrections for Local String Models Stockholm, November 16, 2009 Based on arxiv:0901.4350 (JC), 0906.3297 (JC, Palti) Local vs Global There are many different proposals to realise Standard
More informatione θ 1 4 [σ 1,σ 2 ] = e i θ 2 σ 3
Fermions Consider the string world sheet. We have bosons X µ (σ,τ) on this world sheet. We will now also put ψ µ (σ,τ) on the world sheet. These fermions are spin objects on the worldsheet. In higher dimensions,
More informationThink Globally, Act Locally
Think Globally, Act Locally Nathan Seiberg Institute for Advanced Study Quantum Fields beyond Perturbation Theory, KITP 2014 Ofer Aharony, NS, Yuji Tachikawa, arxiv:1305.0318 Anton Kapustin, Ryan Thorngren,
More informationASPECTS OF FREE FERMIONIC HETEROTIC-STRING MODELS. Alon E. Faraggi
ASPECTS OF FREE FERMIONIC HETEROTIC-STRING MODELS Alon E. Faraggi AEF, 990 s (top quark mass, CKM, MSSM w Cleaver and Nanopoulos) AEF, C. Kounnas, J. Rizos, 003-009 AEF, PLB00, work in progress with Angelantonj,
More informationPrarit Agarwal (Seoul National University) International winter school : "Partition Functions and Automorphic Forms", 2018
Prarit Agarwal (Seoul National University) International winter school : "Partition Functions and Automorphic Forms", 2018 Based on 1. N=1 Deformations and RG Flows of N=2 SCFTs - J. Song, K. Maruyoshi
More informationCentral charges and RG flow of strongly-coupled N = 2 theory
arxiv:30.020v [hep-th] 2 Jan 203 Central charges and RG flow of strongly-coupled N = 2 theory Dan Xie and Peng Zhao Institute for Advanced Study, Einstein Dr., Princeton, NJ 08540, USA DAMTP, University
More informationHilbert Series and Its Applications to SUSY Gauge Theories
Hilbert Series and Its Applications to SUSY Gauge Theories NOPPADOL MEKAREEYA Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) Progress in Quantum Field Theory and String Theory April 2012 Noppadol
More informationThe exact quantum corrected moduli space for the universal hypermultiplet
The exact quantum corrected moduli space for the universal hypermultiplet Bengt E.W. Nilsson Chalmers University of Technology, Göteborg Talk at "Miami 2009" Fort Lauderdale, December 15-20, 2009 Talk
More informationSupercurrents. Nathan Seiberg IAS
Supercurrents Nathan Seiberg IAS 2011 Zohar Komargodski and NS arxiv:0904.1159, arxiv:1002.2228 Tom Banks and NS arxiv:1011.5120 Thomas T. Dumitrescu and NS arxiv:1106.0031 Summary The supersymmetry algebra
More informationThe Dirac-Ramond operator and vertex algebras
The Dirac-Ramond operator and vertex algebras Westfälische Wilhelms-Universität Münster cvoigt@math.uni-muenster.de http://wwwmath.uni-muenster.de/reine/u/cvoigt/ Vanderbilt May 11, 2011 Kasparov theory
More informationYet Another Alternative to Compactification
Okayama Institute for Quantum Physics: June 26, 2009 Yet Another Alternative to Compactification Heterotic five-branes explain why three generations in Nature arxiv: 0905.2185 [hep-th] Tetsuji KIMURA (KEK)
More informationSCFTs, Compact CY 3-folds, and Topological Strings
SCFTs, Compact CY 3-folds, and Topological Strings Patrick Jefferson (to appear) in collaboration with: Hirotaka Hayashi, Hee-Cheol Kim, Kantaro Ohmori, and Cumrun Vafa This subject of this talk is SCFTs
More informationExact Solutions of 2d Supersymmetric gauge theories
Exact Solutions of 2d Supersymmetric gauge theories Abhijit Gadde, IAS w. Sergei Gukov and Pavel Putrov UV to IR Physics at long distances can be strikingly different from the physics at short distances
More informationPartition functions of N = 4 Yang-Mills and applications
Partition functions of N = 4 Yang-Mills and applications Jan Manschot Universität Bonn & MPIM ISM, Puri December 20, 2012 Outline 1. Partition functions of topologically twisted N = 4 U(r) Yang-Mills theory
More informationSeiberg-Witten Theories on Ellipsoids Kazuo Hosomichi (YITP)
Seiberg-Witten Theories on Ellipsoids Kazuo Hosomichi (YITP) with Naofumi Hama, arxiv: 1206.6359 Introduction AGT relation (2009) : a correspondence between 2D CFTs 4D N=2 SUSY (Liouville / Toda) (SW)
More informationF-theory effective physics via M-theory. Thomas W. Grimm!! Max Planck Institute for Physics (Werner-Heisenberg-Institut)! Munich
F-theory effective physics via M-theory Thomas W. Grimm Max Planck Institute for Physics (Werner-Heisenberg-Institut) Munich Ahrenshoop conference, July 2014 1 Introduction In recent years there has been
More informationF-theory and the classification of elliptic Calabi-Yau manifolds
F-theory and the classification of elliptic Calabi-Yau manifolds FRG Workshop: Recent progress in string theory and mirror symmetry March 6-7, 2015 Washington (Wati) Taylor, MIT Based in part on arxiv:
More informationCounting black hole microstates as open string flux vacua
Counting black hole microstates as open string flux vacua Frederik Denef KITP, November 23, 2005 F. Denef and G. Moore, to appear Outline Setting and formulation of the problem Black hole microstates and
More informationA Solvable Irrelevant
A Solvable Irrelevant Deformation of AdS $ / CFT * A. Giveon, N. Itzhaki, DK arxiv: 1701.05576 + to appear Strings 2017, Tel Aviv Introduction QFT is usually thought of as an RG flow connecting a UV fixed
More informationIntroduction to Orientifolds.
Introduction to Orientifolds http://www.physto.se/~mberg Overview Orientability in Quantum Field Theory: spinors S R(2π) ψ = ψ Orientability in Quantum Field Theory: spinors (S R(2π) ) 2 ψ =+ ψ S R(2π)
More information1. Introduction and statement of results This paper concerns the deep properties of the modular forms and mock modular forms.
MOONSHINE FOR M 4 AND DONALDSON INVARIANTS OF CP ANDREAS MALMENDIER AND KEN ONO Abstract. Eguchi, Ooguri, and Tachikawa recently conjectured 9] a new moonshine phenomenon. They conjecture that the coefficients
More informationLocalization & Exact Quantum Entropy
Localization & Exact Quantum Entropy Atish Dabholkar CERN, Geneva Centre National de la Recherche Scientifique Université Pierre et Marie Curie Paris VI Progress in QFT and String Theory 6 April 2012 Atish
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 informationTopological vertex and quantum mirror curves
Topological vertex and quantum mirror curves Kanehisa Takasaki, Kinki University Osaka City University, November 6, 2015 Contents 1. Topological vertex 2. On-strip geometry 3. Closed topological vertex
More informationFrom Little Strings to M5-branes via a Quasi-Topological Sigma Model on Loop Group
From Little Strings to M5-branes via a Quasi-Topological Sigma Model on Loop Group Meng-Chwan Tan National University of Singapore String and M-Theory: The New Geometry of the 21st Century Meng-Chwan Tan
More informationLecture 12 Holomorphy: Gauge Theory
Lecture 12 Holomorphy: Gauge Theory Outline SUSY Yang-Mills theory as a chiral theory: the holomorphic coupling and the holomorphic scale. Nonrenormalization theorem for SUSY YM: the gauge coupling runs
More informationCoupling Selection Rules in Heterotic Orbifold Compactifications
Coupling Selection Rules in Heterotic Orbifold Compactifications Susha L. Parameswaran Leibniz Universität Hannover JHEP 1205 (2012) 008 with Tatsuo Kobayashi, Saúl Ramos-Sánchez & Ivonne Zavala see also
More informationInstanton calculus for quiver gauge theories
Instanton calculus for quiver gauge theories Vasily Pestun (IAS) in collaboration with Nikita Nekrasov (SCGP) Osaka, 2012 Outline 4d N=2 quiver theories & classification Instanton partition function [LMNS,
More informationMapping 6D N=1 supergravities to F-theory
Mapping 6D N=1 supergravities to F-theory The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation As Published Publisher Kumar, Vijay,
More informationA Dissertation DAN XIE
ASPECTS OF FOUR DIMENSIONAL N = 2 FIELD THEORY A Dissertation by DAN XIE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of
More informationAnomaly and gaugino mediation
Anomaly and gaugino mediation Supergravity mediation X is in the hidden sector, P l suppressed couplings SUSY breaking VEV W = ( W hid (X) + W vis ) (ψ) f = δj i ci j X X ψ j e V ψ 2 i +... Pl τ = θ Y
More information