Perturbed Defects and T-Systems in Conformal Field Theory

TL;DR

This paper explores how perturbing defect lines in conformal field theory with chiral defect fields leads to operators obeying T-systems, connecting defect theory with integrable models.

Contribution

It demonstrates that perturbed defect operators satisfy T-system relations in conformal field theories with su(2)-type fusion rules, with applications to minimal models and Liouville theory.

Findings

Perturbed defect operators obey T-system functional relations.

Application to Virasoro minimal models and Liouville theory.

Establishment of a link between defect perturbations and integrable models.

Abstract

Defect lines in conformal field theory can be perturbed by chiral defect fields. If the unperturbed defects satisfy su(2)-type fusion rules, the operators associated to the perturbed defects are shown to obey functional relations known from the study of integrable models as T-systems. The procedure is illustrated for Virasoro minimal models and for Liouville theory.