A form factor approach to finite temperature correlation functions in $c=1$ CFT

TL;DR

This paper develops a form factor approach using Jack polynomials to compute finite temperature correlation functions in $c=1$ conformal field theories, demonstrating rapid convergence and accurate low- and high-temperature limits.

Contribution

It introduces a novel form factor expansion method for $c=1$ CFTs using Jack polynomials, enabling efficient computation of finite temperature correlations.

Findings

Rapid convergence of the form factor expansion to exact results.

Low-temperature behavior captured by (p+1)-particle form factors.

High-temperature limit approximated with states of up to 3 particles.

Abstract

The excitation spectrum of specific conformal field theories (CFT) with central charge $c=1$ can be described in terms of quasi-particles with charges $Q=-p,+1$ and fractional statistics properties. Using the language of Jack polynomials, we compute form factors of the charge density operator in these CFTs. We study a form factor expansion for the finite temperature density-density correlation function, and find that it shows a quick convergence to the exact result. The low-temperature behavior is recovered from a form factor with $p+1$ particles, while the high-temperature limit is recovered from states containing no more than 3 particles.