Orbifolds and topological defects
Ilka Brunner, Nils Carqueville, Daniel Plencner
TL;DR
This work develops a universal defect-based framework for orbifolds of two-dimensional field theories, replacing traditional symmetry-group constructions by symmetry defects $A_G=igoplus_{g in G}{}_g I$ and, more generally, by separable Frobenius algebras $A$ in a bicategory to realise generalized orbifolds. It shows how NS and RR sectors, bulk-boundary data, and disc correlators can be captured via defect networks and adjunction structures, linking the physical content to Hochschild (co)homology and Serre functors, and it elaborates a generalized Cardy condition for open/closed TFTs. In Landau-Ginzburg models the defect perspective reproduces conventional twisted sectors, enables efficient computation of RR brane charges and superpotential terms, and extends to non-supersymmetric or non-group-based orbifolds. The authors develop a rigorous bicategorical algebra framework, define generalized twisted sectors as $ ext{HH}^ullet(A)$ and $ ext{HH}_ullet(A)$, and analyze the resulting open/closed theory, including defect actions and fusion compatibility, highlighting when a full TFT structure is recovered (e.g., for symmetric $A$). Overall, the paper broadens orbifold theory beyond classical symmetry groups, connecting defect-based constructions to deep algebraic invariants and paving the way for fully extended TFT interpretations in 2D quantum field theories.
Abstract
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau-Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction also works in the absence of supersymmetry and for generalised "orbifolds" that need not arise from symmetry groups. In general this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.