Discontinuity relations for the AdS(4)/CFT(3) correspondence

TL;DR

This paper investigates the analytic structure of TBA equations in the AdS(4)/CFT(3) correspondence, deriving functional relations for discontinuities that could lead to new methods for calculating the spectrum.

Contribution

It derives the jump discontinuity relations for Y functions in the AdS(4)/CFT(3) case, extending the analytic framework similar to AdS(5)/CFT(4).

Findings

Discontinuity relations encode the analytic structure of Y functions.

Relations are similar to those in AdS(5)/CFT(4).

Results may enable alternative nonlinear integral equations.

Abstract

We study in detail the analytic properties of the Thermodynamic Bethe Ansatz (TBA) equations for the anomalous dimensions of composite operators in the planar limit of the 3D N=6 superconformal Chern-Simons gauge theory and derive functional relations for the jump discontinuities across the branch cuts in the complex rapidity plane. These relations encode the analytic structure of the Y functions and are extremely similar to the ones obtained for the previously-studied AdS(5)/CFT(4) case. Together with the Y-system and more basic analyticity conditions, they are completely equivalent to the TBA equations. We expect these results to be useful to derive alternative nonlinear integral equations for the AdS(4)/CFT(3) spectrum.