Fermionic Basis in Conformal Field Theory: The Free Fermion Point
Sergei Adler, Hermann Boos
TL;DR
This paper derives an explicit master function at the free-fermion point of the six-vertex model and uses the ODE/IM correspondence to incorporate local integrals of motion into the conformal-field-theory limit. Through a detailed scaling analysis of Baxter's TQ-relations, it provides a concrete integral representation for the master function and demonstrates how the fermionic basis yields exact correlation functions of fermionic descendants via the relation $\omega^{\text{sc}}(\lambda,\mu)=\delta_λ^-\delta_μ^-\Phi(λ,μ)$. The authors connect the fermionic construction to Virasoro generators, compute explicit level-2 and level-4 coefficients, and verify consistency with known equal-boundary and reflection-relations results, including principal-value integral treatments. The work advances the lattice-to-CFT dictionary by encoding integrals of motion within the fermionic basis at $\nu=\tfrac{1}{2}$ and outlines clear directions for generalizing beyond the free-fermion point and to more general boundary conditions, with potential impact on precise CFT observables from integrable lattice models.
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 $ω(λ, μ)$ 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.