't Hooft Anomaly Matching Conditions for Generalized Symmetries in 2D

TL;DR

This paper extends 't Hooft anomaly matching conditions to 2D theories with generalized symmetries, providing a new proof that encompasses a broad class of internal and spacetime symmetries.

Contribution

It offers a simplified proof of anomaly matching in 2D for theories with diverse generalized symmetries, including higher spin and space-time symmetries.

Findings

Validates anomaly matching for a wide class of 2D symmetries

Includes non-abelian and higher spin symmetries in the analysis

Provides a new, simplified proof method

Abstract

The 't Hooft anomaly matching conditions are a standard tool to study and test non-perturbative issues in quantum field theory. We give a new, simple proof of the anomaly matching conditions in 2D Poincare` invariant theories. We consider the case of invariance under a large class of generalized symmetries, which include abelian and non-abelian internal symmetries, space-time symmetries generated by the stress tensor, and W-type of symmetries generated by higher spin currents.