Conformal interfaces between free boson orbifold theories

TL;DR

This work develops a comprehensive framework for conformal interfaces between $c=1$ theories, namely free bosons on $S^1$ and their $\mathbb{Z}_2$ orbifolds, by building Cardy-consistent boundary states in $c=2$ product theories and applying the unfolding trick to produce explicit interfaces. It systematically constructs both factorized and non-factorized interfaces, including rotated branes and their orbifold extensions, and analyzes their fusion algebra to identify invertible topological interfaces corresponding to global symmetries and marginal deformations. The paper provides detailed fusion rules, including gcd-based compositions and explicit topological criteria, illuminating how interfaces compose to realize symmetry actions, isomorphisms, and radius-changing deformations. It also discusses gaps (such as missing isomorphisms at special radii) and outlines future directions to achieve a more complete classification of interfaces among $c=1$ theories and to extend the framework to broader classes of CFTs and RG flows.

Abstract

We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c=2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent theory.