't Hooft anomalies and boundaries

TL;DR

The paper investigates the limitations of placing theories with 't Hooft anomalies on manifolds with boundaries, revealing that most anomalies are incompatible with boundaries unless specific conditions are met, especially in two-dimensional conformal field theories.

Contribution

It establishes new constraints on 't Hooft anomalies in boundary settings and extends known results about chiral matter quantization in Lagrangian theories.

Findings

An obstruction exists for theories with 't Hooft anomalies on manifolds with boundaries.

Most anomalies, except the trace anomaly, are incompatible with boundaries in 2D conformal field theories.

Lagrangian theories with chiral matter cannot be canonically quantized under mild assumptions.

Abstract

We argue that there is an obstruction to placing theories with 't Hooft anomalies on manifolds with a boundary, unless the symmetry associated with the anomaly can be represented as a non-invariance under an Abelian transformation. For a two dimensional conformal field theory we further demonstrate that all anomalies except the usual trace anomaly are incompatible on a manifold with a boundary. Our findings extend a known result whereby, under mild assumptions, Lagrangian theories with chiral matter cannot be canonically quantized.