TY - JOUR

T1 - Rigid holography and six-dimensional (Formula presented.) theories on AdS5 × S1

AU - Aharony, Ofer

AU - Berkooz, Micha

AU - Rey, Soo-Jong

N1 - Israel Science Foundation center for excellence grant; Minerva foundation; Federal German Ministry for Education and Research; I-CORE program of the Planning and Budgeting Committee; Israel Science Foundation [1937/12]; Henri Gutwirth award from the Henri Gutwirth Fund for the Promotion of Research; ISF within the ISF-UGC joint research program framework [1200/14]; National Research Foundation of Korea(NRF) grant - Korea government(MSIP) through Seoul National University [2005-0093843, 2010-220-C00003, 2012K2A1A9055280]We would like to thank Michael Douglas, Nadav Drukker, Jaume Gomis, Rajesh Gopakumar, Sergei Gukov, Marc Henneaux, Stefan Hohenegger, Amer Iqbal, David Kutasov, Albion Lawrence, Shlomo Razamat, Joerg Teschner, Cumrun Vafa and Misha Vasiliev for useful discussions. We especially thank Zohar Komargodski and Yuji Tachikawa for many useful discussions and comments on a draft of this paper. The work of OA and MB was supported in part by an Israel Science Foundation center for excellence grant, by the Minerva foundation with funding from the Federal German Ministry for Education and Research, and by the I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). OA is the Samuel Sebba Professorial Chair of Pure and Applied Physics, and he is supported also by a Henri Gutwirth award from the Henri Gutwirth Fund for the Promotion of Research, and by the ISF within the ISF-UGC joint research program framework (grant no. 1200/14). SJR was supported in part by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) through Seoul National University with grant numbers 2005-0093843, 2010-220-C00003 and 2012K2A1A9055280.

PY - 2015/3/24

Y1 - 2015/3/24

N2 - Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A(K-1) superconformal field theory (SCFT) on AdS(5)xS(1), with equal radii for AdS(5) and for S-1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS(5)xS(5)/Z(K). On R(4,1)xS(1), this six-dimensional theory has a 5(K-1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS(5)xS(1), the theory has a 2(K-1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS(5) whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS(5). Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS(5)xS(1) with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories’ on AdS5 × S 1.

AB - Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A(K-1) superconformal field theory (SCFT) on AdS(5)xS(1), with equal radii for AdS(5) and for S-1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS(5)xS(5)/Z(K). On R(4,1)xS(1), this six-dimensional theory has a 5(K-1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS(5)xS(1), the theory has a 2(K-1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS(5) whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS(5). Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS(5)xS(1) with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories’ on AdS5 × S 1.

UR - http://www.scopus.com/inward/record.url?scp=84961290777&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/JHEP03(2015)121

DO - https://doi.org/10.1007/JHEP03(2015)121

M3 - مقالة

SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

ER -