Fermionic Basis in Conformal Field Theory: The Free Fermion Point

TL;DR

This paper explores the fermionic basis in conformal field theory at the free fermion point, deriving explicit formulas for expectation values and describing the Virasoro module using the master function approach.

Contribution

It introduces an explicit form of the master function for the free fermion point and details the Virasoro module structure including integrals of motion.

Findings

Explicit master function form derived

Asymptotic expansion of expectation values computed

Complete Virasoro module description achieved

Abstract

In this work, we use the master function approach to describe the CFT limit of the six-vertex model at the free fermion point. Using the ODE/IM correspondence, we obtain an explicit form of the master function. This allows us to compute the asymptotic expansion of the function $\omega(\lambda, \mu)$ describing the expectation values of the fermionic basis operators. As a result, we describe the entire Virasoro module of the corresponding CFT, including the integrals of motion as well.