Vacuum Expectation Values from a variational approach

TL;DR

The paper tackles the problem of determining Vacuum Expectation Values in perturbed two-dimensional conformal field theories, where IR divergences hinder naive perturbation theory. It extends the Truncated Conformal Space approach into a variational framework on a cylinder to obtain nonperturbative VEV constants for UV-regular operators via a double limit $R,N → ∞$. The authors apply the method to the Ising model (M(3)) and Tricritical Ising model (M(4)) with several perturbations and compare with exact results from the Thermodynamic Bethe Ansatz and Lukyanov–Zamolodchikov, finding good agreement and providing new estimates. This work demonstrates a practical route to access short-distance data in perturbed CFTs without requiring integrability, with potential to map all UV-regular VEVs and refine OPE-based analyses.

Abstract

In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator. As an example we estimate the VEV's of all (UV regular) primary operators of the Ising model and of some of the Tricritical Ising Model conformal field theories when perturbed by any choice of the relevant primary operators. We compare our results with some other independent predictions.