Gapped theories have torsion anomalies

TL;DR

This paper proves that gapped theories with certain boundary conditions have finite order in the group of invertible field theories, using evaluations in parametrized families.

Contribution

It establishes a connection between gapped theories with boundary conditions and their finite order in the invertible field theory group, extending previous conjectures.

Findings

Gapped theories with projectively topological boundaries have finite order.

Uses evaluations of field theories in parametrized families for proofs.

Provides evidence supporting a broader conjecture in field theory classification.

Abstract

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for `projectively topological'. Our proofs use evaluations of a field theory in parametrized families.