Defect lines, dualities, and generalised orbifolds

TL;DR

Defect lines in 2D CFTs are used to study symmetries and dualities, and to construct generalized orbifolds. The paper develops a defect-centered framework where defect operators $D_X$ capture interface physics and defects can be conformal or topological; topological defects admit a fusion algebra that mirrors Virasoro fusion rules in many models. A central result is that a 3-cocycle $[\psi] \in H^3(G, \mathbb{C}^\times)$ associated to the group of group-like defects governs obstructions to orbifolding by subgroups $H$, with discrete torsion given by $H^2(H, \mathbb{C}^\times)$. The authors show that any rational CFT with left-right symmetry $V$ and suitable genus-0/1 data is a generalized orbifold of Cardy, realized by a defect network of a topological defect $Q$ and described via special symmetric Frobenius algebras, thereby unifying exceptional modular invariants under a single framework.

Abstract

Defects are a useful tool in the study of quantum field theories. This is illustrated in the example of two-dimensional conformal field theories. We describe how defect lines and their junction points appear in the description of symmetries and order-disorder dualities, as well as in the orbifold construction and a generalisation thereof that covers exceptional modular invariants.