Duality and defects in rational conformal field theory

TL;DR

This paper investigates topological defect lines in rational conformal field theory, revealing how they encode symmetries and dualities, with a detailed example involving the c=4/5 models like the Ising and Potts models.

Contribution

It introduces a framework for analyzing phase boundaries and defects in rational CFTs, linking defect properties to symmetries and dualities, including explicit examples.

Findings

Defects are topologically invariant under continuous deformations.

Phase boundaries encode symmetries and dualities in CFT.

Explicit analysis of c=4/5 models illustrates the concepts.

Abstract

We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting one-dimensional phase boundaries can be used to extract symmetries and order-disorder dualities of the CFT. The case of central charge c=4/5, for which there are two inequivalent world sheet phases corresponding to the tetra-critical Ising model and the critical three-states Potts model, is treated as an illustrative example.