Superstrings on NS5 backgrounds, deformed AdS₃ and holography

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-deformed SL(2, ℝ)} × SU(2) × T⁴ 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) × T⁴/ℤ₂. This allows us to compute the partition functions for the J³ J̄³ and J²J̄² 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.