B-field in AdS(3)/CFT(2) Correspondence and Integrability

TL;DR

The paper constructs a topological Wess-Zumino term for permutation supercoset sigma-models relevant to AdS3/CFT2 and shows that integrability, kappa-symmetry, and conformal invariance are equivalent under a specific coupling relation κ^2 = 1 − χ^2. It derives a Lax pair demonstrating classical integrability, analyzes the one-loop beta function to confirm conformality for AdS3-based cosets, and computes the BMN-like mass spectrum in a light-cone gauge to illustrate flux-induced mass shifts. The work also clarifies the NSNS/WZW limit and quantization of the WZ coefficient, and outlines future paths toward algebraic-curve methods, Bethe ansatz, and connections to worldsheet CFT for a broader class of AdS3 backgrounds with mixed flux.

Abstract

We construct topological Wess-Zumino term for supercoset sigma-models on various AdS(3) backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappa-symmetry and conformal invariance are equivalent to each other.

Figures (1)

• Figure 1: One loop contributions to the beta-function. The dashed lines denote derivatives acting on propagators.