Gauging anomalous unitary operators

TL;DR

This paper explores how quantum anomalies can characterize obstructions in realizing boundary theories of topological phases and Floquet systems, focusing on time-reversal and mixed symmetry anomalies in various dimensions.

Contribution

It introduces a framework for using quantum anomalies to quantify obstructions in boundary unitary operators of topological and Floquet systems, including new examples involving time-reversal and mixed symmetries.

Findings

Time-reversal symmetric boundary unitaries exhibit anomalies when gauging KMS symmetry.

Mixed anomalies between U(1) and discrete symmetries are identified in boundary operators.

The framework applies to systems in different spatial dimensions, revealing new topological features.

Abstract

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as C and CP, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.