Integrability and the AdS 3/CFT 2 correspondence

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 $ {\mathbb{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.