Superstrings on NS5 backgrounds, deformed AdS3and holography

We study a non-standard decoupling limit of the D1/D5-brane system, whichinterpolates between the near-horizon geometry of the D1/D5 background and thenear-horizon limit of the pure D5-brane geometry. The S-dual description ofthis background is actually an exactly solvable two-dimensional (worldsheet)conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This modelis free of strong-coupling singularities. By a careful treatment of theSL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain thefull partition function for superstrings on SL(2,R) x SU(2) x K3. This allowsus to compute the partition functions for the J^3 and J^2 current-currentdeformations, as well as the full line of supersymmetric null deformations,which links the SL(2,R) conformal field theory with linear dilaton theory. Theholographic interpretation of this setup is a renormalization-group flowbetween the decoupled NS5-brane world-volume theory in the ultraviolet (LittleString Theory), and the low-energy dynamics of super Yang--Mills string-likeinstantons in six dimensions.Comment: JHEP style, 59 pages, 1 figure; v2: minor changes, to appear in JHE