Integrability and the AdS3/CFT2 correspondence

We investigate the AdS(3)/CFT2 correspondence for theories with 16 supercharges using the integrability approach. We construct Green-Schwarz actions for Type IIB strings on AdS(3) x S-3 x M-4 where M-4 = T-4 or S-3 x S-1 using the coset approach. These actions are based on a Z(4) automorphism of the super-coset D(2, 1; alpha) x D(2, 1; alpha)/SO(1, 2) x SO(3) x 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 alpha = 0, 1/2, 1 we propose a set of quantum Bethe equations valid at all values of the coupling. The AdS(3)/CFT2 duals contain novel massless modes whose role remains to be explored.