Abstract:We investigate the AdS 3 /CFT 2 correspondence for theories with 16 supercharges using the integrability approach. We construct Green-Schwarz actions for Type IIB strings on AdS 3 × S 3 × M 4 where M 4 = T 4 or S 3 × S 1 using the coset approach. These actions are based on a Z 4 automorphism of the super-coset D(2, 1; α)×D(2, 1; α)/SO(1, 2)× SO(3) × SO(3). The equations of motion admit a representation in terms of a Lax connection, showing that the system is classically integrable. We present the finite gap equations for these actions. When α = 0 , 1/2 , 1 we propose a set of quantum Bethe equations valid at all values of the coupling. The AdS 3 /CFT 2 duals contain novel massless modes whose role remains to be explored.

Abstract:We study superstrings on AdS 3 × S 3 × T 4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and write down a set of finite-gap equations that describe the massive part of the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-FrolovStaudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantisation of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.

We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold G/H are known to be classically integrable. We investigate a possibility to extend an argument of absence of quantum anomalies in non local current conservation from non super case to the case of supergroup manifolds which are asymptotically free in one