Two-dimensional conformal field theories on AdS2d+ 1 backgrounds

Journal of High Energy Physics, 1999

Various exact two-dimensional conformal field theories with AdS 2d+1 target space are constructed. These models can be solved using bosonization techniques. Some examples are presented that can be used in building perturbative superstring theories with AdS backgrounds, including AdS 5 .

Journal of High Energy Physics, 2021

We present a new infinite family of Type IIB backgrounds with an AdS2 factor, preserving $$ \mathcal{N} $$ N = 4 SUSY. For each member of the family we propose a precise dual Super Conformal Quantum Mechanics (SCQM). We provide holographic expressions for the number of vacua (the “central charge”), Chern-Simons terms and other non-perturbative aspects of the SCQM. We relate the “central charge” of the one-dimensional system with a combination of electric and magnetic fluxes in Type IIB. The Ramond-Ramond fluxes are used to propose an extremisation principle for the central charge. Other physical and geometrical aspects of these conformal quantum mechanics are analysed.

2000

We study the unitary supermultiplets of the N = 8 d = 5 anti-de Sitter (AdS) superalgebra SU(2,2|4) which is the symmetry algebra of the IIB string theory on AdS5 × S5. We give a complete classification of the dou- bleton supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond to d = 4 conformal field theories

Nuclear Physics B, 1998

We study the unitary supermultiplets of the N = 8 d = 5 anti-de Sitter (AdS) superalgebra SU (2, 2|4) which is the symmetry algebra of the IIB string theory on AdS 5 × S 5 . We give a complete classification of the doubleton supermultiplets of SU (2, 2|4) which do not have a Poincare limit and correspond to d = 4 conformal field theories (CFT) living on the boundary of AdS 5 . The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d = 4 N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N = 4 conformal supergravity in d = 4 which can be coupled to N = 4 super Yang-Mills theory in d = 4. We also study the "massless" supermultiplets of SU (2, 2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate "massless" supermultiplet is the N = 8 graviton supermultiplet in AdS 5 . The other "massless" supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.

1998

We study the unitary supermultiplets of the N = 8 d = 5 anti-de Sitter (AdS) superalgebra SU (2, 2|4) which is the symmetry algebra of the IIB string theory on AdS 5 × S 5. We give a complete classification of the dou-bleton supermultiplets of SU (2, 2|4) which do not have a Poincare limit and correspond to d = 4 conformal field theories (CFT) living on the boundary of AdS 5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d = 4 N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N = 4 conformal supergravity in d = 4 which can be coupled to N = 4 super Yang-Mills theory in d = 4. We also study the " massless " supermultiplets of SU (2, 2|4) which can be obtained by tensoring two dou-bleton supermultiplets. The CPT s...

Journal of High Energy Physics, 2004

The Coulomb gas representation of expectation values in SU (2) conformal field theory developed by Dotsenko is extended to the SL(2, R) WZW model and applied to bosonic string theory on AdS 3 and to Type II superstrings on AdS 3 × N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string states in arbitrary winding sectors are calculated. Scattering amplitudes that violate winding number conservation are also discussed.

2012

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative '1/N ' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be wellapproximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program.

Modern Physics Letters A, 2001

We review recent progress in understanding the anti-de Sitter/conformal field theory correspondence in the context of two-dimensional dilaton gravity theory.

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 ×S 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 × S 5 /Z K. On R 4,1 × S 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 × S 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 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2

1999

We construct string target spacetimes with AdS 3 × X geometry, which have an N = 2 spacetime superconformal algebra. X is found to be a U (1) fibration over a manifold which is a target for an N = 2 worldsheet conformal field theory. We emphasize theories with free field realizations where in principle it is possible to compute the full one-particle string spectrum. *