On $AdS_2/CFT_1$ transfer matrices, Bethe ansatz and scale invariance

TL;DR

This paper computes transfer-matrix eigenvalues in the massless sector of an $AdS_2$ integrable model, derives Bethe ansatz equations, and explores their implications for scale invariance and underlying 2D critical theories.

Contribution

It provides explicit eigenvalue calculations, conjectures a general pattern, and formulates Bethe ansatz equations for massless sectors in $AdS_2$ integrable systems.

Findings

Eigenvalues computed for up to 5 particles in the massless sector.

Conjectured general pattern for transfer-matrix eigenvalues.

Derived Bethe ansatz equations applicable to relativistic and non-relativistic cases.

Abstract

We explicitly calculate the $AdS_2 \times S^2 \times T^6$ transfer-matrix eigenvalues in the massless sector using the exact integrable S-matrix, for up to 5 particles. This enables us to conjecture the general pattern. We use the conjectured form of the eigenvalues to write down a set of massless Bethe ansatz equations. The same procedure applies to the relativistic as well as to the non-relativistic situation. In the relativistic case, the right and left modes decouple. We speculate that the relativistic massless Bethe ansatz we obtain in that case might capture the integrable structure of an underlying 2D critical theory. We finally take advantage of some remarkable simplifications to make progress in the massive case as well.