't Hooft anomalies and boundaries

TL;DR

The paper proves that 't Hooft anomalies are obstructed on manifolds with boundaries unless the anomaly is Abelian or Abelian-mixed, using the Wess-Zumino consistency framework and anomaly descent. It analyzes anomalies across dimensions, showing in 4D and higher that non-Abelian or pure gravitational anomalies cannot consistently live on spaces with boundaries, while Abelian cases can with suitable boundary terms; in 2D, it demonstrates that boundary CFTs cannot support flavor or gravitational anomalies and that c_L = c_R and k_L = k_R are required. A complementary 2D CFT analysis on the half-plane reinforces the absence of boundary anomalies, tying the constraints to conformal and Ward identities. The results have implications for quantization of chiral matter, RG flows, and entanglement studies in theories with boundaries, and suggest directions for extending the analysis to discrete symmetries.

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.