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

Nikolay Gromov, Fedor Levkovich-Maslyuk

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.

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

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.

Paper Structure

This paper contains 21 sections, 135 equations.

Table of Contents

  1. Introduction
  2. Asymptotic large $L$ solution of Y-system
  3. Asymptotic Bethe ansatz equations for physical ${\rm AdS}_4/{\rm CFT}_3$
  4. General asymptotic solution
  5. Asymptotic solution in scaling limit
  6. TBA equations for ${\rm AdS}_4/{\rm CFT}_3$
  7. Ground state TBA equations for ${\rm AdS}_4/{\rm CFT}_3$.
  8. Y-system from TBA equations
  9. Integral equations for excited states
  10. Solution of the Y-system in the scaling limit
  11. Y-system equations in the scaling limit
  12. Asymptotics of Y-functions
  13. Solution in upper and right wings
  14. Matching wings
  15. The spectrum from Y-system
  16. ...and 6 more sections