# A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases

## TL;DR

This paper investigates the emergence of mixed global anomalies at critical points between bosonic symmetry-protected phases, revealing how short-range entanglement and symmetry considerations lead to novel critical phenomena.

## Contribution

It provides a general argument for emergent $bZ_2$ symmetries with mixed anomalies at phase transitions in symmetry-protected phases, including explicit anomaly criteria and cocycle representatives.

## Key findings

- Emergent $bZ_2$ symmetry at critical points
- Identification of conditions for mixed global anomalies
- Connections to (2+1)d beyond-Landau critical points

## Abstract

Symmetry-protected phases are gapped phases of matter which are distinguished only in the presence of a global symmetry G. These quantum phases lack any symmetry-breaking or topological order, and have short-range entangled ground states. Based on this short-range entanglement property, we give a general argument for the existence of an emergent unitary or anti-unitary $\mathbb{Z}_2$ symmetry at a critical point separating two different bosonic symmetry-protected phases in any dimension. Often, the emergent symmetry group at criticality has a mixed global anomaly. For those phases classified by group cohomology, we identify a criterion for when such a mixed global anomaly is present, and write down representative cocycles for the corresponding anomaly class. We illustrate our results with a series of examples, and make connections to recent results on (2 + 1)-d beyond-Landau critical points.