Finite Density States in Integrable Conformal Field Theories

TL;DR

The paper investigates energies of states at large charge density in integrable conformal field theories, focusing on conformal coset models. It develops the finite-density Bethe ansatz in the conformal limit, solving for right- and left-moving sectors and their energy- and charge-densities, and then analyzes two distinct realizations of the O(2) model: the massless Thirring description and the N→2 limit of the O(N) sigma model. The authors show that the N→2 limit introduces a nontrivial zero-mode sector, complicating the conformal Bethe equations, and extend the construction to the OSp(2+2M|2M) coset by lifting the N→2 limit of the O(N) S-matrix. They discuss the challenges of finite-volume corrections and outline a program toward a full integrable description relevant for AdS/CFT, including identifying the PSU(2,2|4) S-matrix and BRST structure.

Abstract

We study states of large charge density in integrable conformal coset models. For the O(2) coset, we consider two different S-matrices, one corresponding to a Thirring mass perturbation and the other to the continuation to O(2+epsilon). The former leads to simplification in the conformal limit; the latter gives a more complicated description of the O(2) system, with a large zero mode sector in addition to the right- and left-movers. We argue that for the conformal O(2+2M|2M) supergroup coset, the S-matrix is given by the analog of the O(2+epsilon) construction.