Integrability and the AdS(3)/CFT(2) correspondence

TL;DR

This paper explores the integrability of the AdS(3)/CFT(2) correspondence with 16 supercharges, constructing string actions, demonstrating classical integrability, and proposing quantum Bethe equations, revealing new massless modes.

Contribution

It constructs Green-Schwarz actions for AdS(3) backgrounds, shows classical integrability via a Lax connection, and introduces quantum Bethe equations for the duality.

Findings

Classical integrability established through Lax connection.

Finite gap equations derived for the string actions.

Quantum Bethe equations proposed for specific parameter values.

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)xS(3)xM(4) where M(4)=T(4) or S(3)xS(1) using the coset approach. These actions are based on a Z(4) automorphism of the super-coset D(2,1;alpha)xD(2,1;alpha)/SO(1,2)xSO(3)xSO(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)/CFT(2) duals contain novel massless modes whose role remains to be explored.