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

TL;DR

This work develops a nonperturbative framework for the planar AdS$_4$/CFT$_3$ spectrum by formulating all-loop Bethe Ansatz equations for the mirror theory in the ${ m sl}(2|1)$ grading, proposing a comprehensive string hypothesis for bound states, and deriving the ground-state Thermodynamic Bethe Ansatz equations and the corresponding Y-system. The approach leverages the mirror transformation and Yang–Yang type minimization to connect finite-size effects to the spectrum on a circle, incorporating two magnon species A and B with BES-type dressing and intricate bound-state structures. A key outcome is a set of coupled integral equations for pseudoenergies and a universal Y-system, whose structure is richer and more intricate than in AdS$_5$/CFT$_4$ due to the multi-valued Y-functions and mixed-type nodes. The results pave the way for excited-state analyses and deepen the understanding of analytic properties and dressing factors in the AdS$_4$/CFT$_3$ integrability program, with potential cross-links to GKVI and future numerical checks.

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.