Massive symmetric tensor field on AdS
|
|
- Dina Donna Waters
- 6 years ago
- Views:
Transcription
1 Massive symmetric tensor field on AdS Aleksey Polishchuk Steklov Mathematical Institute, Gubkin str.8, GSP-1, , Moscow, Russia arxiv:hep-th/99548v4 1 Oct 1999 Abstract The two-point Green function of a local operator in CFT corresponding to a massive symmetric tensor field on the AdS background is computed in the framework of the AdS/CF T correspondence. The obtained two-point function is shown to coincide with the two-point function of the graviton in the limit when the AdS mass vanishes. 1 Introduction The AdS/CFT correspondence conjectured in [1] states that in the large N limit and at large t Hooft coupling λ = gy MN the classical supergravity/m-theory on the Anti-de Sitter space AdS times a compact manifold is dual to a certain SUN conformal gauge theory CFT defined on the boundary of AdS. One notable example of this correspondence being the duality between D = 4, N = 4 supersymmetric Yang-Mills theory and D = 1 Type IIB supergravity theory on AdS 5 S 5. The precise formulation of the conjecture was given in [], [3] where it was proposed to identify the generating functional for connected Green functions of local operators in CFT with the on-shell value of the supergravity action under the restriction that the supergravity fields satisfy the Dirichlet conditions on the boundary of AdS. Recall that in the standard representation of AdS as an upper-half space x >, x k R, k = 1,...d with the metric ds = g µν dx µ dx ν = 1 dx dx + dx i dx i, x the boundary includes the plane x = as well as the point x =. Since the boundary is located infinitely far away from any point in the interior the supergravity action is infrared divergent and must be regularized. As was pointed out in [4] the consistent regularization procedure with respect to Ward identities requires one to shift the boundary of AdS to the surface in the interior defined by x = ε. Then the Dirichlet boundary value problem for supergravity fields is properly defined and one can compute the on-shell value of the supergravity action as a functional of the boundary fields. With the account of this regularization procedure the standard formulation of the AdS/CFT correspondence assumes the form: Ox 1 Ox n = lim ε alexey@mi.ras.ru δ δφ 1 x 1 δ δφ n x n S on shell φ 1 x 1,..., φ n x n φi x i =φ i x =ε,x i, 1
2 where x i are some points on the boundary of AdS d+1, O i x i are gauge invariant composite operators in CFT and φ i x i are the corresponding supergravity fields. Here we used the convention in which the coordinates x µ of AdS d+1 are split according to: x = x,x, so that x R d. The action S on shell is the sum of the bulk supergravity action and the boundary terms necessary to make the AdS/CFT correspondence complete. The origin of these boundary terms was elucidated in [5] where it was shown that they appear in passing from the Hamiltonian description of the bulk action to the Lagrangian one. The AdS/CFT correspondence has been tested by computing various two- and three-point functions of local operators in D = 4, N = 4 supersymmetric Yang-Mills theory on AdS 5. In particular two-point functions corresponding to scalars [3] - [8], vectors [3], [4], [9], [1], spinors [1] - [1], the Rarita-Schwinger field [13] - [16], antisymmetric form fields [17] - [] and the graviton [5], [1], [] were computed on the AdS background. The only field in the supergravity spectrum, found in [3], that has evaded the attention is the massive symmetric second-rank tensor field. In this paper we fill in the gap by computing the remaining two-point Green function. We note that the Dirichlet boundary value problem for the massive symmetric tensor field is nontrivial due to the fact that the equations of motion for various components are coupled. Furthermore, in computing the two-point Green function we have to stick with the regularization procedure described above in order to obtain the consistent result. At the end of our computation we find that in the limit when the AdS mass vanishes the correlation function reduces to that of the massless symmetric tensor field, i.e. the graviton. Equations of motion The starting point in the calculation is the action for the symmetric second-rank tensor φ µν on AdS d+1 [4] 1 : S [φ µν ] = 1 1 d d+1 x g κ AdS 4 λφ λ φ 1 4 λφ µν λ φ µν 1 µ φ ν µ ν φ + 1 µφ µν λ +φ λν d φ µνφ µν + d 4 φ 1 4 m φ µν φ µν 1 4 m φ,.1 where g is the determinant of the AdS metric g µν. The action.1 leads to the following equations of motion [3], [4] λ λ φ µ ν + m φ µ ν =,. φ µ µ =, µφ µ ν =..3 The massive terms in.1 destroy the standard symmetry: δφ µν = µ ξ ν + ν ξ µ, which is present in the case of the massless symmetric tensor field. As a result of this symmetry breaking one can no longer perform gauge fixing. Since φ µ ν is traceless, we can eliminate the component φ from the equations of motion by using the constraint φ +φ i i =. Let us introduce a concise notation: φ = φ i i, ϕi = φ i, ϕ = iϕ i. 1 Note that the AdS background satisfies restriction 1 of [4] and also to simplify our calculations we set the parameter ξ of [4] equal to 1.
3 Then starting from.,.3 one can obtain the following system of coupled differential equations ϕ = d + 1 φ,.4 x d + 1 ϕ i + k φ i k =,.5 x d + 3 d m φ =..6 x x x Here eq..6 corresponds to µ = ν = in. while eqs..4 and.5 follow from.3. To simplify the notation, we chose the convention in which indices are raised and lowered with the flat metric δ µν = x g µν so that, in particular, = δ µν µ ν. The Fourier mode for the field φ vanishing at x is given by: Here k = k, and K is a modified Bessel functions [5]: K z = π I z I z sin π φx,k = Aε,kx d + K kx..7 d = + m,, I z = k= 1 z +k. k!γ + k + 1 Recall that the modified Bessel function satisfies the recurrence relations [5]: K +1 z K 1 z = z K z, K +1 z + K 1 z = d dz K z..8 By differentiating.5 with respect to x i and using.4 and.6 one gets: d 1 i j φ i j = + x d 1d + + m φ..9 x From.7 and.9 we can easily deduce the Fourier mode solution for the field πx,k k i k j φ i j x,k = = Aε,k x d d 1x kk +1 x k x k K x k, where recurrence formulae.8 were used. Here we introduced a concise notation = d, + = d +. 3
4 Taking the ratio of φ and π at x = ε results in the following relation πk = ε d 1εkK +1εk εk K εk K εk φk, where πk = πε,k and, similarly for other fields. In the limit ε, πk ε φk and therefore if we keep πk finite as ε, then φk will tend to zero. On the other hand, keeping φk finite leads to the divergence of πk. Consequently, we ought to fix π at x = ε. Thus we have: φx,k = x d + ε d πx,k = x d ε d K x k d 1εkK +1 εk εk K εk πk,.1 d 1x kk +1 x k x k K x k πk. d 1εkK +1 εk εk K εk.11 The Fourier mode solution for the field ϕ is found by substituting.1 into.4: ϕx,k = x d +1 1 K x k x kk +1 x k πk,.1 ε d d 1εkK +1 εk εk K εk where once again recurrence formulae.8 were used. Next we turn our attention to the field ϕ i. Here we need to use equation m x ϕ i + x i φ = k φ i k,.13 which follows from i-component of. by taking into account.5. Now we decompose ϕ i into the transversal and longitudinal parts: ϕ i = ϕ i i ϕ. Rewriting.5 and.13 for the transversal part of ϕ i leads to: ϕ m i = x k φ k i i l m φ l m,.14 d + 1 ϕ i = k φ k i x i l m φ l m..15 By differentiating.15 with respect to x and taking into account.14 we obtain an homogeneous differential equation for the field ϕ i : d d m x x x 4 ϕ i =..16
5 The Fourier mode solution is given by: ϕ i x,k = B i ε,k x d +1 K x k..17 To find B i ε,k substitute.17 into.15 to obtain the following formula k l φ l i x,k k i k πx,k = ib i ε,k x d x kk +1 x k + K x k..18 Taking the ratio of.18 and.17 at x = ε we find: k l φ i l ki εkk +1 εk k kπk = iε 1 K εk + K εk ϕ i k. Using the same arguments as before one finds that in order to avoid the divergence at ε the solutions for the field ϕ i and k l φ l i k i π should take the following form k ϕ i x,k = iε x d +1 K x k k l φ i ε d εkk +1 εk + K εk lk ki k πk,.19 k l φ i l x,k ki k πx,k = x d x kk +1 x k + K x k k l φ i ki ε d l k εkk +1 εk + K εk k πk.. Setting µ = i, ν = j in. and taking into account.3 we arrive at the following equation d 1 + m x x Let us introduce the transversal traceless part of φ i j: φ i j = j ϕ i + i δ ϕ j + j i φ..1 x x φ i j = φi j 1 i k φ k j 1 j k φ i k + 1 i j k m φ k m + 1 i j d 1 δi j φ k l φk l.. Rewriting.1 for the transversal traceless part yields: d 1 + m x x φ i j =..3 The Fourier mode solution of eq..3 is φ i jx,k = x d ε d Taking into account.,.4,.1,.11, and. we obtain: K x k K εk φ i jk..4 [ φ i j x,k = x K x k ε K εk φ i j k + K +1x k + K x k k i k l K +1 εk + K εk k φl j k + k jk l k φi l k 5
6 ki k j k πk + d 1K x k x k K x k 4 d 1K εk εk K εk ki k j k πk 1 k i k j δ i 4 d 1 k j x k K x k d 1εkK +1 εk εk K εk d 1K x k x k ] K x k πk,.5 d 1K εk εk K εk k while taking into account.19 and.1 gives: [ x 1+ K x k ϕ i x,k = iε k l φ l i ε K +1 εk + K εk k k i k πk ] 1 K x k K +1 x k k i d 1K +1 εk εk K εk k πk,.6 where we introduced a concise notation: K z = z K z. 3 Two-point Green function To compute the Green function in the framework of the AdS/CF T correspondence we need to evaluate the on-shell value of the action. Taking into account equations of motion. and.3 one finds that the on-shell value of.1 is S on shell = ε d+1 8κ x =ε d d x φ i j φ j i φ φ + φϕ ϕ k i φ i k + d + 1 ε φ + ϕ k ϕ k. Let us first consider the contribution to S on shell that depends locally on boundary fields, i.e. does not contain the normal derivative. We expect that such terms do not contribute to the non-local part of S on shell. So we need to consider the behavior of φ and ϕ k on the boundary of AdS. To this end we note that according to.1 the field φk is local since K εk d 1εkK +1 εk εk K εk = Oε k, while expanding solution.6 in ε gives: [ 1 ϕ i k = iε k l φ i ki l k k πk k i ] + k πk + local. 3.1 Here we included only non-local terms. In deriving 3.1 use was made of the power series expansion of the modified Bessel function [5]: K z = 1 z Γ , 3. 6
7 where ellipsis indicate terms of order z 4 and higher which evidently lead to local expressions as well as terms of order z + which will become negligible in the limit ε. From expression 3.1 it follows that ϕ i k is a local field. Consequently, the terms in 3.1 that depend only on the value of fields at the boundary do not contribute to the non-local part of S on shell as we expected. Next we consider terms with the normal derivative. In evaluating such terms it is useful to employ the following identity d dx x ε γ Fx k Fεk = γ x ε + k ε =ε d ln Fkε. 3.3 dk Taking into account solution.1, identity 3.3 and expansion 3. we find that φε,x is equal to d d k + φε,x = + Oεk ε 1 π de ikx ε Oε k πk. Clearly φ is a local expression and therefore does not contribute to the non-local part of S on shell. Consequently, the non-local part is entirely determined by the following expression ε d+1 d d xφ j d d k 8κ ix x =ε π de ikx φ i j x,k. 3.4 Taking into account solution.5, identity 3.3 and expansion 3. we see that the expression for φ i j gets three different contributions: the first contribution comes from differentiating the ratio x ε raised to the power or + ; the second contribution comes from Oεk terms in the power expansion of the logarithmic derivative of various functions in.5 and the third contribution comes from Oε 1 k terms in the same expansion. From.5 we can easily read off the first contribution which is equal to ε φ i jk + k i k l ε k φl jk + k jk l k φi lk ki k j k πk + k i k j 4 ε k πk 4 1 k i k j + δ i d 1 k j εk 1 ε πk ε k = k i k j ε πk + local, 3.5 d 1 k where we took into account the expansion of φ i j into the transversal and longitudinal parts given by.. Next, Oεk terms from the power series expansion of the logarithmic derivative give: εk [ 1 1 φ i j k + + k i k l 1 + k φl j k + k jk l k φi l k k j ki k πk k i k j k πk 1 k i k j δ i εk 4 d 1 k j ] πk k = k i k j ε πk + local, 3.6 d 1 k
8 where we used 3. and.. Adding together 3.6 and 3.5, the non-local part cancels leading to a purely local expression which does not contribute to the non-local part of S on shell. Finally, Oε 1 k terms in the expansion of the logarithmic derivative give: Here, η ε 1 k [ φ i j k + = η ε 1 k [ + 1 d 1 + φ i j k + k i k l k φl j k + k jk l k φi l k k j ki k πk 4 k i ] k j δ i 1 πk k j k k i k l k φl j k+ +k jk l k φi l k η = Γ1 1 Γ k i k j k πk k i ] k j k πk In the process of deriving 3.7 we dropped all terms containing δj i since such terms are negligible in the limit ε. To understand why this is so, note that when δj i is contracted with φj ix from 3.4 it gives the trace of φ i j x which according to.1 is order Oε at x = ε. Now putting together 3.4 and 3.7 we arrive at the following formula for S on shell S on shell [φ i j ] = ηε d d d xd d y Φ j 8κ ixφ r s y d d k k π de ikx y [ 1 δi r δs j + 1 δis δ jr k i k r + k δs j + ki k s k δ jr + k jk s k δi r + k jk r k δis + 1 ki k j k r k s + k rk s k 4 k δi j + ki k j k δs r + ] d δi jδr s, 3.8 where we introduced the traceless part of φ i j: Φ i j x = φi j x δi j d φx. In order to complete the calculation of the two-point Green function we need to evaluate the integral over k in 3.8. To this end, we employ the standard formula for the Fourier transformation of generalized functions [6]: d d k de ikxki1 k i k in k δ = δ n Γ π k n d+δ n π d/ Γ δ+n i n 1 i1 i in x d+δ n. 3.9 With the help of 3.9 we find that the non-local part of the on shell value of the action is equal to: S on shell [φ i j] = C d, ε d d d xd d y Φj ixφ r s y [ 1 x y +d Ji rx yjj s x y ] + 1 Jis x yj jr x y 1 d δi j δr s, 8
9 where we introduced J i jx = δ i j xi x j x and C d, = + + 1Γ + π d κ + 1Γ. 3.1 From this we can easily deduce the two-point function of local operators in the boundary CFT corresponding to the massive symmetric traceless rank two tensor field Φ i j : [ < Oj i xos r y >= C d, 1 x y +d Ji r x yjs j x y + 1 Jis x yj jr x y 1 ] d δi j δs r. Here we performed rescaling in order to remove the regularization parameter ε. Note that in the limit m or, equivalently, d, the obtained expression correctly reproduces the two-point function corresponding to the massless symmetric tensor field graviton [5], [1], []. ACKNOWLEDGEMENT The author would like to thank S.Frolov and G.Arutyunov for valuable discussions and A.Slavnov for the support during the preparation of the manuscript. References [1] J. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, Adv. Theor. Math. Phys , hep-th/9711. [] S. S. Gubser,I. R. Klebanov and A. M. Polyakov, Gauge Theory Correlators from Non-critical String Theory, Phys. Lett. B , hep-th/9819. [3] E. Witten, Anti De Sitter Space and Holography, Adv. Theor. Math. Phys , hepth/9815. [4] D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, hep-th/ [5] G.Arutyunov and S.Frolov, On the origin of supergravity boundary terms in the AdS/CF T correspondence, hep-th/ [6] W. Mück and K. S. Viswanathan, Conformal Field Theory Correlators from Classical Scalar Field Theory on AdS d+1, Phys. Rev. D , hep-th/ [7] L. Chekhov, AdS/CFT correspondence on torus, hep-th/ [8] I.Ya. Arefeva and I.V. Volovich, On large N conformal field theories, field theories in anti-de Sitter space and singletons, hep-th/9838. [9] G. Chalmers, H. Nastase, K. Schalm and R. Siebelink, R-Current Correlators in N = 4 Super Yang-Mills Theory from Anti-de Sitter Supergravity, hep-th/ [1] W. Mück and K. S. Viswanathan, Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields, Phys. Rev. D , hep-th/
10 [11] M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B , hep-th/ [1] A.M. Chezelbash, K. Kaviani, S. Parvizi, A.H. Fatollahi, Interacting Spinors-Scalars and AdS/CF T Correspondence, Phys. Lett. B , hep-th/ [13] S. Corley, The massless gravitino and the AdS/CFT correspondence, hep-th / [14] A. Volovich, Rarita-Schwinger Field in the AdS/CF T Correspondence, JHEP , hep-th/9899. [15] A.S.Koshelev and O.A.Rytchkov, Note on the Massive Rarita-Schwinger Field in the AdS/CFT correspondence, Phys. Lett. B , hep-th/ [16] W. Mück and K. S. Viswanathan, The AdS/CF T Correspondence for the Massive Rarita- Schwinger Field, hep-th/ [17] G. E. Arutyunov and S. A. Frolov, Antisymmetric tensor field on AdS 5, hep-th/ [18] W. S. l Yi, Generating functionals of correlation functions of p-form currents in AdS/CFT correspondence, hep-th/ [19] W. S. l Yi, Correlators of currents corresponding to the massive p-form field in AdS/CFT correspondence, hep-th/ [] P. Minces and V.O. Rivelles, Chern-Simons Theories in the AdS/CF T Correspondence, hep-th/9913. [1] H. Liu and A. A. Tseytlin, D = 4 Super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, hep-th/98483, to appear in NPB. [] W. Mück and K. S. Viswanathan, The Graviton in the AdS-CFT correspondence: Solution via the Dirichlet boundary value problem, hep-th/ [3] H.J.Kim, L.J.Romans, P.van Nieuwenhuizen, Mass spectrum of chiral ten-dimensional N = supergravity on S 5, Phys. Rev. D [4] I.L.Buchbinder, V.A.Krykhtin and V.D. Pershin, On consistent equations of motion for massive spin- field coupled to gravity in string theory, hep-th/9988 [5] I.S.Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products. Academic Press, fifth edn [6] I.M. Gel fand and G.E. Shilov, Generalized functions, 1-st vol., in Russian [7] G.Arutyunov and S.Frolov, Quadratic action for type II B supergravity on AdS 5 S 5, hep-th/ [8] G.M. Sotkov and R.P. Zaikov, Conformal Invariant two and three- point functions for fields with arbitrary spin, Rep. on Math. Phys
Scalar Field Theory in the AdS/CFT Correspondence Revisited
Scalar Fiel Theory in the AS/CFT Corresponence Revisite arxiv:hep-th/9907079v4 Feb 000 Pablo Minces an Victor. Rivelles Universiae e São Paulo, Instituto e Física Caixa Postal 66.38 - CEP 0535-970 - São
More informationHolographic Wilsonian Renormalization Group
Holographic Wilsonian Renormalization Group JiYoung Kim May 0, 207 Abstract Strongly coupled systems are difficult to study because the perturbation of the systems does not work with strong couplings.
More informationChapter 3: Duality Toolbox
3.: GENEAL ASPECTS 3..: I/UV CONNECTION Chapter 3: Duality Toolbox MIT OpenCourseWare Lecture Notes Hong Liu, Fall 04 Lecture 8 As seen before, equipped with holographic principle, we can deduce N = 4
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 informationMassive Spinors and ds/cft Correspondence
Massive Spinors and ds/cft Correspondence Farhang Loran arxiv:hep-th/00135v3 16 Jun 00 Department of Physics, Isfahan University of Technology IUT) Isfahan, Iran, Institute for Studies in Theoretical Physics
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 informationBoundary multi-trace deformations and OPEs in AdS/CFT correspondence
CERN-TH/00-01 hep-th/00158 Boundary multi-trace deformations and OPEs in AdS/CFT correspondence Anastasios C. Petkou 1 CERN Theory Division, CH-111 Geneva 3, Switzerland Abstract We argue that multi-trace
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More informationOne Loop Tests of Higher Spin AdS/CFT
One Loop Tests of Higher Spin AdS/CFT Simone Giombi UNC-Chapel Hill, Jan. 30 2014 Based on 1308.2337 with I. Klebanov and 1401.0825 with I. Klebanov and B. Safdi Massless higher spins Consistent interactions
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 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 informationarxiv:hep-th/ v3 24 Apr 2007
Anti-de Sitter boundary in Poincaré coordinates C. A. Ballón Bayona and Nelson R. F. Braga Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 Brazil Abstract
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 informationarxiv:hep-th/ v1 28 Jan 1999
N=1, D=10 TENSIONLESS SUPERBRANES II. 1 arxiv:hep-th/9901153v1 28 Jan 1999 P. Bozhilov 2 Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia We consider a model for tensionless (null)
More informationSome Geometrical Problems in AdS/CFT
Some Geometrical Problems in AdS/CFT Eric D Hoker Mathematics Colloquium 2006 May 10, Columbia University 1 Outline I. What is the AdS/CFT correspondence? N = 4 Super Yang-Mills theory; Type IIB String
More information8.821 F2008 Lecture 12: Boundary of AdS; Poincaré patch; wave equation in AdS
8.821 F2008 Lecture 12: Boundary of AdS; Poincaré patch; wave equation in AdS Lecturer: McGreevy Scribe: Francesco D Eramo October 16, 2008 Today: 1. the boundary of AdS 2. Poincaré patch 3. motivate boundary
More informationBPS non-local operators in AdS/CFT correspondence. Satoshi Yamaguchi (Seoul National University) E. Koh, SY, arxiv: to appear in JHEP
BPS non-local operators in AdS/CFT correspondence Satoshi Yamaguchi (Seoul National University) E. Koh, SY, arxiv:0812.1420 to appear in JHEP Introduction Non-local operators in quantum field theories
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 informationGlueballs and AdS/CFT
Preprint typeset in JHEP style - PAPER VERSION hep-ph/yymmnnn Glueballs and AdS/CFT John Terning T-8 MS B285, Los Alamos National Lab., Los Alamos NM, 87545 Email: terning@lanl.gov Abstract: I review the
More informationarxiv:hep-th/ v2 6 Jan 2004
hep-th/0310063 January 2004 arxiv:hep-th/0310063v2 6 Jan 2004 The group approach to AdS space propagators: A fast algorithm Thorsten Leonhardt, Werner Rühl Fachbereich Physik, TU Kaiserslautern Postfach
More informationA Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula
A Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula Arshad Momen and Tapobrata Sarkar the Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11 4014 Trieste, Italy
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.81 String Theory Fall 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.81 F008 Lecture 1: Boundary of AdS;
More informationFeynman and Wheeler Scalar Field Propagators in the ADS/CFT Correspondence
arxiv:8.03473v [hep-th] 7 Nov 08 Feynman and Wheeler Scalar Field Propagators in the ADS/CFT Correspondence A. Plastino,3,4, M.C.Rocca,,3 Departamento de Física, Universidad Nacional de La Plata, Departamento
More informationKatrin Becker, Texas A&M University. Strings 2016, YMSC,Tsinghua University
Katrin Becker, Texas A&M University Strings 2016, YMSC,Tsinghua University ± Overview Overview ± II. What is the manifestly supersymmetric complete space-time action for an arbitrary string theory or M-theory
More informationHIGHER SPIN ADS 3 GRAVITIES AND THEIR DUAL CFTS
HIGHER SPIN ADS 3 GRAVITIES AND THEIR DUAL CFTS Yasuaki Hikida (Keio University) Based on [1] JHEP02(2012)109 [arxiv:1111.2139 [hep-th]] [2] arxiv:1209.xxxx with Thomas Creutzig (Tech. U. Darmstadt) Peter
More informationGraviton contributions to the graviton self-energy at one loop order during inflation
Graviton contributions to the graviton self-energy at one loop order during inflation PEDRO J. MORA DEPARTMENT OF PHYSICS UNIVERSITY OF FLORIDA PASI2012 1. Description of my thesis problem. i. Graviton
More informationGlueballs at finite temperature from AdS/QCD
Light-Cone 2009: Relativistic Hadronic and Particle Physics Instituto de Física Universidade Federal do Rio de Janeiro Glueballs at finite temperature from AdS/QCD Alex S. Miranda Work done in collaboration
More informationTwistor Strings, Gauge Theory and Gravity. Abou Zeid, Hull and Mason hep-th/
Twistor Strings, Gauge Theory and Gravity Abou Zeid, Hull and Mason hep-th/0606272 Amplitudes for YM, Gravity have elegant twistor space structure: Twistor Geometry Amplitudes for YM, Gravity have elegant
More informationAnomalous dimensions at strong coupling
Anomalous dimensions at strong coupling Luca Mazzucato Simons Center for Geometry and Physics Stony Brook University Stony Brook, US NY 11794-3636 Brenno Carlini Vallilo Departamento de Ciencias Físicas,
More informationHolographic Entanglement Entropy for Surface Operators and Defects
Holographic Entanglement Entropy for Surface Operators and Defects Michael Gutperle UCLA) UCSB, January 14th 016 Based on arxiv:1407.569, 1506.0005, 151.04953 with Simon Gentle and Chrysostomos Marasinou
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 informationBulk versus boundary quantum states
Bulk versus boundary quantum states Henrique Boschi-Filho and Nelson R. F. Braga Instituto de Física, Universidade Federal do Rio de Janeiro Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil Abstract
More informationarxiv:hep-th/ v1 21 May 1996
ITP-SB-96-24 BRX-TH-395 USITP-96-07 hep-th/xxyyzzz arxiv:hep-th/960549v 2 May 996 Effective Kähler Potentials M.T. Grisaru Physics Department Brandeis University Waltham, MA 02254, USA M. Roče and R. von
More informationV Finite T, probe branes, quarks, other extensions
Introduction to the AdS/CFT correspondence Outline I CFT review II AdS/CFT correspondence III Large N review IV D3 branes and AdS 5 S 5 V Finite T, probe branes, quarks, other extensions 1 0 References
More informationMinkowski correlation functions in AdS/CFT
Preprint typeset in JHEP style - HYPER VERSION Minkowski correlation functions in AdS/CFT James Charbonneau Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada, V6T
More informationHolographic Geometries from Tensor Network States
Holographic Geometries from Tensor Network States J. Molina-Vilaplana 1 1 Universidad Politécnica de Cartagena Perspectives on Quantum Many-Body Entanglement, Mainz, Sep 2013 1 Introduction & Motivation
More informationSTOCHASTIC QUANTIZATION AND HOLOGRAPHY
STOCHASTIC QUANTIZATION AND HOLOGRAPHY WORK WITH D.MANSI & A. MAURI: TO APPEAR TASSOS PETKOU UNIVERSITY OF CRETE OUTLINE CONFORMAL HOLOGRAPHY STOCHASTIC QUANTIZATION STOCHASTIC QUANTIZATION VS HOLOGRAPHY
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 informationThe boundary S-matrix and the AdS to CFT dictionary
hep-th/9903048 The boundary S-matrix and the AdS to CFT dictionary arxiv:hep-th/9903048v2 1 Oct 1999 Steven B. Giddings Department of Physics University of California Santa Barbara, CA 93106-9530 Abstract
More informationAn Introduction to AdS/CFT Correspondence
An Introduction to AdS/CFT Correspondence Dam Thanh Son Institute for Nuclear Theory, University of Washington An Introduction to AdS/CFT Correspondence p.1/32 Plan of of this talk AdS/CFT correspondence
More informationNTNU Trondheim, Institutt for fysikk
FY3464 Quantum Field Theory II Final exam 0..0 NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory II Contact: Kåre Olaussen, tel. 735 9365/4543770 Allowed tools: mathematical
More informationarxiv:hep-th/ v1 28 Nov 1999
UCLA/99/TEP/46 SU-ITP-99-5 hep-th/99mmnnn The Operator Product Expansion of N = 4 SYM and the 4 point Functions of Supergravity arxiv:hep-th/99v 8 Nov 999 Eric D Hoker a, Samir D. Mathur b, Alec Matusis
More informationTwo-Form Fields and the Gauge Theory Description of Black Holes. Abstract
Two-Form Fields and the Gauge Theory Description of Black Holes hep-th/9803082 SLAC-PUB-7767 March 1998 Arvind Rajaraman Stanford Linear Accelerator Center, Stanford, CA 94309 Abstract We calculate the
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationPOMERON and AdS/CFT CORRESPONDENCE FOR QCD. Chung-I Tan. Physics Department, Brown University, Providence RI 02912, USA,
POMERON and AdS/CFT CORRESPONDENCE FOR QCD Chung-I Tan Physics Department, Brown University, Providence RI 02912, USA, E-mail: tan@het.brown.edu The Maldacena conjecture that QCD is holographically dual
More informationGauge/Gravity Duality at Finite N
Gauge/Gravity Duality at Finite N Badr Awad Elseid Mohammed A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the
More informationThe Conformal Algebra
The Conformal Algebra Dana Faiez June 14, 2017 Outline... Conformal Transformation/Generators 2D Conformal Algebra Global Conformal Algebra and Mobius Group Conformal Field Theory 2D Conformal Field Theory
More informationth Aegean Summer School / Paros Minás Tsoukalás (CECs-Valdivia)
013-09-4 7th Aegean Summer School / Paros Minás Tsoukalás (CECs-Valdivia Higher Dimensional Conformally Invariant theories (work in progress with Ricardo Troncoso 1 Modifying gravity Extra dimensions (string-theory,
More informationAsymptotic Symmetries and Holography
Asymptotic Symmetries and Holography Rashmish K. Mishra Based on: Asymptotic Symmetries, Holography and Topological Hair (RKM and R. Sundrum, 1706.09080) Unification of diverse topics IR structure of QFTs,
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 informationWeyl anomaly for Wilson surfaces
SPIN-1999/12 Göteborg ITP 99-05 hep-th/9905163 Weyl anomaly for Wilson surfaces Måns Henningson 1 and Kostas Skenderis 2 Institute of Theoretical Physics, Chalmers University of Technology, S-412 96 Göteborg,
More informationarxiv:hep-ph/ v1 8 Feb 2000
Gravity, Particle Physics and their Unification 1 J. M. Maldacena Department of Physics Harvard University, Cambridge, Massachusetts 02138 arxiv:hep-ph/0002092v1 8 Feb 2000 1 Introduction Our present world
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 informationds/cft Contents Lecturer: Prof. Juan Maldacena Transcriber: Alexander Chen August 7, Lecture Lecture 2 5
ds/cft Lecturer: Prof. Juan Maldacena Transcriber: Alexander Chen August 7, 2011 Contents 1 Lecture 1 2 2 Lecture 2 5 1 ds/cft Lecture 1 1 Lecture 1 We will first review calculation of quantum field theory
More informationarxiv:hep-th/ v4 29 Dec 2005
Glueball Regge trajectories from gauge/string duality and the Pomeron Henrique Boschi-Filho, Nelson R. F. Braga, and Hector L. Carrion Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa
More informationStrings in flat space and pp waves from N = 4 Super Yang Mills
hep-th/0202021 arxiv:hep-th/0202021v3 26 Feb 2002 Strings in flat space and pp waves from N = 4 Super Yang Mills David Berenstein, Juan Maldacena and Horatiu Nastase Institute for Advanced Study, Princeton,
More informationQuantum Nambu Geometry in String Theory
in String Theory Centre for Particle Theory and Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK E-mail: chong-sun.chu@durham.ac.uk Proceedings of the Corfu Summer Institute
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 informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 998971 Allowed tools: mathematical tables 1. Spin zero. Consider a real, scalar field
More informationContact interactions in string theory and a reformulation of QED
Contact interactions in string theory and a reformulation of QED James Edwards QFT Seminar November 2014 Based on arxiv:1409.4948 [hep-th] and arxiv:1410.3288 [hep-th] Outline Introduction Worldline formalism
More informationIf I only had a Brane
If I only had a Brane A Story about Gravity and QCD. on 20 slides and in 40 minutes. AdS/CFT correspondence = Anti de Sitter / Conformal field theory correspondence. Chapter 1: String Theory in a nutshell.
More informationTopological Ward Identity and. Anti-de Sitter Space/CFT Correspondence
APCTP/98-16 Topological Ward Identity and Anti-de Sitter Space/CFT Correspondence Taejin Lee Asia Pacific Center for Theoretical Physics, 207-43 Cheongryangri-dong Dongdaemun-gu, Seoul 130-012, Korea and
More informationQGP, Hydrodynamics and the AdS/CFT correspondence
QGP, Hydrodynamics and the AdS/CFT correspondence Adrián Soto Stony Brook University October 25th 2010 Adrián Soto (Stony Brook University) QGP, Hydrodynamics and AdS/CFT October 25th 2010 1 / 18 Outline
More informationExercise 1 Classical Bosonic String
Exercise 1 Classical Bosonic String 1. The Relativistic Particle The action describing a free relativistic point particle of mass m moving in a D- dimensional Minkowski spacetime is described by ) 1 S
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 informationGeneralized N = 1 orientifold compactifications
Generalized N = 1 orientifold compactifications Thomas W. Grimm University of Wisconsin, Madison based on: [hep-th/0602241] Iman Benmachiche, TWG [hep-th/0507153] TWG Madison, Wisconsin, November 2006
More informationGeometrical Approximation to the AdS/CFT Correspondence
International Journal of Advanced Research in Physical Science (IJARPS) Volume 3, Issue 6, 2016, PP 26-30 ISSN 2349-7874 (Print) & ISSN 2349-7882 (Online) www.arcjournals.org Geometrical Approximation
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 informationHolographic signatures of. resolved cosmological singularities
Holographic signatures of resolved cosmological singularities Norbert Bodendorfer LMU Munich based on work in collaboration with Andreas Schäfer, John Schliemann International Loop Quantum Gravity Seminar
More informationHOLOGRAPHIC RECIPE FOR TYPE-B WEYL ANOMALIES
HOLOGRAPHIC RECIPE FOR TYPE-B WEYL ANOMALIES Danilo E. Díaz (UNAB-Talcahuano) joint work with F. Bugini (acknowledge useful conversations with R. Aros, A. Montecinos, R. Olea, S. Theisen,...) 5TH COSMOCONCE
More informationPutting String Theory to the Test with AdS/CFT
Putting String Theory to the Test with AdS/CFT Leopoldo A. Pando Zayas University of Iowa Department Colloquium L = 1 4g 2 Ga µνg a µν + j G a µν = µ A a ν ν A a µ + if a bc Ab µa c ν, D µ = µ + it a
More informationHow to build a holographic liquid crystal? Piotr Surówka Vrije Universiteit Brussel
How to build a holographic liquid crystal? Piotr Surówka Vrije Universiteit Brussel Euler Symposium On Theoretical And Mathematical Physics, St. Petersburg 17.07.2013 Motivation Hydrodynamics is an effective
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 informationHelicity conservation in Born-Infeld theory
Helicity conservation in Born-Infeld theory A.A.Rosly and K.G.Selivanov ITEP, Moscow, 117218, B.Cheryomushkinskaya 25 Abstract We prove that the helicity is preserved in the scattering of photons in the
More informationPreprint typeset in JHEP style - HYPER VERSION. Special Geometry. Yang Zhang. Abstract: N = 2 Supergravity. based on hep-th/ , Boris PiolineA
Preprint typeset in JHEP style - HYPER VERSION Special Geometry Yang Zhang Abstract: N = Supergravity based on hep-th/06077, Boris PiolineA Contents 1. N = Supergravity 1 1.1 Supersymmetric multiplets
More informationDepartment of Physics
Department of Physics Early time dynamics in heavy ion collisions from AdS/CFT correspondence Anastasios Taliotis taliotis.1@osu.edu based on work done with Yuri Kovchegov arxiv: 0705.1234[hep-ph] The
More informationBaryon Configurations in the UV and IR Regions of Type 0 String Theory
KUCP-038 hep-th/99060 arxiv:hep-th/99060v 7 Sep 999 Baryon Configurations in the UV and IR Regions of Type 0 String Theory Shigenori Seki Graduate School of Human and Environmental Studies Kyoto University,
More informationTESTING ADS/CFT. John H. Schwarz STRINGS 2003
TESTING ADS/CFT John H. Schwarz STRINGS 2003 July 6, 2003 1 INTRODUCTION During the past few years 1 Blau et al. constructed a maximally supersymmetric plane-wave background of type IIB string theory as
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 informationLectures on gauge-gravity duality
Lectures on gauge-gravity duality Annamaria Sinkovics Department of Applied Mathematics and Theoretical Physics Cambridge University Tihany, 25 August 2009 1. Review of AdS/CFT i. D-branes: open and closed
More informationMITOCW watch?v=nw4vp_upvme
MITOCW watch?v=nw4vp_upvme The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To
More informationInheritance principle and Non-renormalization theorems at finite temperature
hep-th/0509117 MIT-CTP-3679 arxiv:hep-th/0509117v2 19 Sep 2005 Inheritance principle and Non-renormalization theorems at finite temperature Mauro Brigante 1, Guido Festuccia 1,2 and Hong Liu 1,2 1 Center
More informationAdS spacetimes and Kaluza-Klein consistency. Oscar Varela
AdS spacetimes and Kaluza-Klein consistency Oscar Varela based on work with Jerome Gauntlett and Eoin Ó Colgáin hep-th/0611219, 0707.2315, 0711.xxxx CALTECH 16 November 2007 Outline 1 Consistent KK reductions
More informationHigher Spin Black Holes from 2d CFT. Rutgers Theory Seminar January 17, 2012
Higher Spin Black Holes from 2d CFT Rutgers Theory Seminar January 17, 2012 Simplified Holography A goal Find a holographic duality simple enough to solve, but complicated enough to look like gravity in
More informationarxiv:hep-th/ v2 13 Sep 2001
Compactification of gauge theories and the gauge invariance of massive modes. Amorim a and J. Barcelos-Neto b Instituto de Física Universidade Federal do io de Janeiro J 21945-97 - Caixa Postal 68528 -
More informationLecture 9: RR-sector and D-branes
Lecture 9: RR-sector and D-branes José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 6, 2013 José D. Edelstein (USC) Lecture 9: RR-sector and D-branes 6-mar-2013
More informationABJM Baryon Stability at Finite t Hooft Coupling
ABJM Baryon Stability at Finite t Hooft Coupling Yolanda Lozano (U. Oviedo) Santiago de Compostela, October 2011 - Motivation: Study the stability of non-singlet baryon vertex-like configurations in ABJM
More informationarxiv: v2 [hep-th] 18 Apr 2017
Twist Two Operator Approach for Even Spin Glueball Masses and Pomeron Regge Trajectory from the Hardwall Model Diego M. Rodrigues 1, Eduardo Folco Capossoli 1,2,, and Henrique Boschi-Filho 1, 1 Instituto
More informationQuantum gravity at one-loop and AdS/CFT
Quantum gravity at one-loop and AdS/CFT Marcos Mariño University of Geneva (mostly) based on S. Bhattacharyya, A. Grassi, M.M. and A. Sen, 1210.6057 The AdS/CFT correspondence is supposed to provide a
More informationSpinning strings and QED
Spinning strings and QED James Edwards Oxford Particles and Fields Seminar January 2015 Based on arxiv:1409.4948 [hep-th] and arxiv:1410.3288 [hep-th] Outline Introduction Various relationships between
More informationTHE ROLE OF BLACK HOLES IN THE ADS/CFT CORRESPONDENCE
THE ROLE OF BLACK HOLES IN THE ADS/CFT CORRESPONDENCE Jakob Gath Submitted in partial fulfilment of the requirements for the degree of Master of Science of the Imperial College London Imperial College
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 informationBeyond the unitarity bound in AdS/CFT
Beyond the unitarity bound in AdS/CFT Tomás Andrade in collaboration with T. Faulkner, J. Jottar, R. Leigh, D. Marolf, C. Uhlemann October 5th, 2011 Introduction 1 AdS/CFT relates the dynamics of fields
More informationTopological DBI actions and nonlinear instantons
8 November 00 Physics Letters B 50 00) 70 7 www.elsevier.com/locate/npe Topological DBI actions and nonlinear instantons A. Imaanpur Department of Physics, School of Sciences, Tarbiat Modares University,
More informationSuperstring in the plane-wave background with RR-flux as a conformal field theory
0th December, 008 At Towards New Developments of QFT and Strings, RIKEN Superstring in the plane-wave background with RR-flux as a conformal field theory Naoto Yokoi Institute of Physics, University of
More informationString Corrections to the Hawking-Page Phase Transition
hep-th/9901143 TUW-99-01 String Corrections to the Hawking-Page Phase Transition Karl Landsteiner Institut für theoretische Physik Technische Universität Wien, TU-Wien Wiedner Hauptstraße 8-10 A-1040 Wien,
More informationGravitational perturbations on branes
º ( Ò Ò ) Ò ± 2015.4.9 Content 1. Introduction and Motivation 2. Braneworld solutions in various gravities 2.1 General relativity 2.2 Scalar-tensor gravity 2.3 f(r) gravity 3. Gravitational perturbation
More informationDimensional reduction
Chapter 3 Dimensional reduction In this chapter we will explain how to obtain massive deformations, i.e. scalar potentials and cosmological constants from dimensional reduction. We start by reviewing some
More informationOn the curious spectrum of duality-invariant higher-derivative gravitational field theories
On the curious spectrum of duality-invariant higher-derivative gravitational field theories VIII Workshop on String Field Theory and Related Aspects ICTP-SAIFR 31 May 2016 Barton Zwiebach, MIT Introduction
More informationBranes at toric conical singularities
Branes at toric conical singularities Dmitri Bykov Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Potsdam-Golm, Germany Steklov Mathematical Institute of
More information