Orbifolds and topological defects

TL;DR

This paper develops a universal framework for studying orbifolds of 2D topological field theories using defects, encompassing supersymmetric and non-supersymmetric cases, and introduces new algebraic structures like Hochschild (co)homology.

Contribution

It introduces a novel, universal defect-based approach to orbifolds in 2D TFTs, extending to non-supersymmetric and generalized orbifolds, with new algebraic insights.

Findings

Unified description of NS and R sectors in orbifold TFTs

Explicit computations for B-twisted Landau-Ginzburg models

Generalization of the Cardy condition and Serre functors

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.