Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model

TL;DR

This paper uses non-linear integral equations to analyze the continuum limit of a lattice model related to the black hole conformal field theory, successfully matching spectra and exploring integrable structures.

Contribution

It rederives the black hole spectrum and numerically matches the spin chain's density of states with the CFT, providing new insights into the integrable structure.

Findings

Rederived the black hole spectrum using NLIEs

Numerically matched the density of states between lattice and CFT

Discussed the integrable structure and perturbations of the black hole CFT

Abstract

It was previously established that the critical staggered XXZ spin chain provides a lattice regularization of the black hole CFT. We reconsider the continuum limit of this spin chain with the exact method of non-linear integral equations (NLIEs), paying particular attention to the effects of a singular integration kernel. With the help of the NLIEs, we rederive the continuous black hole spectrum, but also numerically match the density of states of the spin chain with that of the CFT, which is a new result. Finally, we briefly discuss the integrable structure of the black hole CFT and the identification of its massive integrable perturbation on the lattice.