Topological defects for the free boson CFT

TL;DR

This paper classifies topological defects in free boson conformal field theories on a circle, revealing how T-duality can be interpreted as an order-disorder duality via these defects.

Contribution

It provides a classification of topological defects for free boson CFTs with rational radii and links T-duality to order-disorder duality through defect analysis.

Findings

Classified topological defects for rational radii free bosons.

Demonstrated T-duality as an order-disorder duality via defects.

Abstract

Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order-disorder duality.