Orbifold Construction for Topological Field Theories

TL;DR

This paper introduces a geometric orbifold construction for topological field theories that generalizes existing algebraic orbifoldization methods by functorially relating theories with different symmetry groups.

Contribution

It provides a functorial geometric method to construct new topological field theories from existing ones via group homomorphisms, unifying various orbifold concepts.

Findings

Defines an equivariant topological field theory on a cobordism category.

Provides a functorial construction for pushforward theories under group homomorphisms.

Unifies and generalizes known algebraic orbifoldization techniques.

Abstract

An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite groups assigns in a functorial way to a $G$-equivariant topological field theory an $H$-equivariant topological field theory, the pushforward theory. When $H$ is the trivial group, this yields an orbifold construction for $G$-equivariant topological field theories which unifies and generalizes several known algebraic notions of orbifoldization.