Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3

TL;DR

This paper derives and analyzes TBA equations and the Y-system for the AdS4/CFT3 duality, confirming their consistency and matching with string theory spectra in the strong coupling limit.

Contribution

It provides the derivation of TBA equations for ABJM theory, proposes generalizations for excited states, and demonstrates agreement with string spectra at strong coupling.

Findings

TBA equations for ABJM are derived from mirror Bethe equations.

The Y-system is consistent with TBA for a large subsector.

Complete agreement with string spectra at strong coupling.

Abstract

We study the exact spectrum of the AdS4/CFT3 duality put forward by Aharony, Bergman, Jafferis and Maldacena (ABJM). We derive thermodynamic Bethe ansatz (TBA) equations for the planar ABJM theory, starting from "mirror" asymptotic Bethe equations which we conjecture. We also propose generalization of the TBA equations for excited states. The recently proposed Y-system is completely consistent with the TBA equations for a large subsector of the theory, but should be modified in general. We find the general asymptotic infinite length solution of the Y-system, and also several solutions to all wrapping orders in the strong coupling scaling limit. To make a comparison with results obtained from string theory, we assume that the all-loop Bethe ansatz of N.G. and P. Vieira is the valid worldsheet theory description in the asymptotic regime. In this case we find complete agreement, to all orders in wrappings, between the solution of our Y-system and generic quasi-classical string spectrum in AdS3 x S.