TBA and Y-system for planar $AdS_4/CFT_3$

TL;DR

This paper proposes Bethe Ansatz equations and Y-system for the mirror and direct models of the AdS4/CFT3 correspondence, advancing the understanding of integrability in this holographic duality.

Contribution

It introduces the asymptotic Bethe Ansatz equations for the mirror model and derives the TBA equations and Y-system for the AdS4/CFT3 string theory.

Findings

Proposed Bethe Ansatz equations for the mirror model.

Derived TBA equations and Y-system for the direct string theory.

Enhanced the integrability framework for AdS4/CFT3 correspondence.

Abstract

We conjecture the set of asymptotic Bethe Ansatz equations for the {\it mirror} model of the $\text{AdS}_4\times\mathbb{CP}^3$ string theory, corresponding to the planar $\mathcal{N}=6$ superconformal Chern-Simons gauge theory in three dimensions. Hence, we derive the (vacuum energy) thermodynamic Bethe Ansatz equations and the Y-system describing the {\it direct} $\text{AdS}_4/\text{CFT}_3$ string theory.