Superstrings on NS5 backgrounds, deformed AdS₃and holography

Abstract

[a4paper]JHEP3 amsmath,latexsym,amssymb epsfig We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null − def ormedSL(2,R)}×SU (2)× T 4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2, R), based on the better-understood SL(2, R)/U (1) coset, we obtain the full partition function for superstrings on SL(2, R)×SU (2)×T 4 /Z 2 . This allows us to compute the partition functions for the J 3J 3 and J 2J 2 deformations, as well as the full line of supersymmetric null deformations, which links the SL(2, R) conformal field theory with linear-dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (little string theory), and the low-energy dynamics of super Yang-Mills string-like instantons in six dimensions. LPTENS-03/07 document footnote0 footnote section0

The partition function of the supersymmetric two-dimensional black hole and little string theory

“…4 At least for integer level k, the partition function for the single cover is obtained by using instead a Z k+2 orbifold. But, as it is explained in [17], any cover of SL(2, R) gives the same axial coset.…”

“…Apart from these two pieces corresponding to standard characters of the coset, we find new sectors of states which may depend on the regularization procedure. Note that this is not a particular problem of our computation, but would also appear in the bosonic coset partition function [14] , the SL(2, R) partition function [17] (and presumably also in thermal AdS 3 ) if we also consider the exact expansion in characters, with the multiplicities, rather than only the expansion for the zero modes. This is an important open problem that deserves clarification.…”

“…The purely bosonic partition function has been obtained in [17] (following methods in [32] [14]). We refer the reader to these works for more detail.…”

“…To go from the parent theory SL(2, R) to the coset theory SL(2, R)/U (1) we have to remove all the contributions of the U (1) which is gauged. It is known, at least for the bosonic case [18] [17], that it can be done in a modular invariant way by taking an infinite marginal deformation, either R → 0 (axial coset) or R → ∞ (vector coset). In those limits the contribution of the extra U (1) decouples and can be safely removed.…”

String theory: exact solutions, marginal deformations and hyperbolic spaces

“…As a conclusion, the AdS 3 plus plane-wave gravitational background is described in terms of an exact conformal sigma model, that carries two extra background fields: an NS three-form and an electromagnetic two-form. Similarly to the symmetric parabolic deformation [IKP03], the present asymmetric one can be used to construct a space-time supersymmetric background. The SL(2, R) k -CFT treatment of the latter deformation would need the knowledge of the parabolic characters of the affine algebra, not available at present.…”