OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT's

TL;DR

This paper derives formulas for OPE coefficients and the mass-gap in 2D CFTs using integrable scattering descriptions, providing new insights into their structure and deformations.

Contribution

It introduces novel formulas linking integrable scattering data to OPE coefficients and mass-gap relations in specific 2D CFTs.

Findings

Derived formulas for OPE coefficients in Lee-Yang and 3-state Potts models.

Obtained a new mass-gap relation for integrable massive deformations.

Expressed UV energy expansion coefficients in terms of TBA solutions.

Abstract

Many two-dimensional conformal field theories have an alternative integrable scattering description, which reproduces their spectrum of conformal weights. Taking as an example the case of the Lee-Yang nonunitary CFT and the 3-state Potts minimal model, we derive formulas, in terms of their integrable description, for the OPE coefficients of a certain specific primary operator and two identical but otherwise essentially arbitrary operators. As a side result we also obtain a novel formula for the mass-gap relation for the integrable massive deformation of the CFT. These results are obtained through expressing the first nontrivial coefficient in the UV expansion of the energy in terms of the integrable CFT data, i.e. the kink and anti-kink TBA solutions.