Discrete torsion defects

TL;DR

This paper uses the formalism of orbifolding defects to analyze discrete torsion in topological field theories, introducing projective matrix factorisations and demonstrating broader applicability beyond Landau-Ginzburg models.

Contribution

It introduces the concept of projective matrix factorisations for boundary and defect sectors and proves orbifold equivalences in pivotal bicategories, extending the understanding of discrete torsion.

Findings

Re-derivation of known results for Landau-Ginzburg models.

Introduction of projective matrix factorisations for boundary and defect sectors.

Proof that orbifold equivalences hold more generally in topological field theories.

Abstract

Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories. In the case of Landau-Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of `projective matrix factorisations', show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges. Roughly half of our results are not restricted to Landau-Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be obtained by orbifolding via the `quantum symmetry defect'.