Gauging anomalous unitary operators

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 unitary operators at their boundaries which are obstructed. In this paper, we discuss the characterization of such obstruction by using quantum anomalies. As a particular example, we discuss time-reversal symmetric unitary operators in one and two spatial dimensions, by gauging 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 boundaries of topological Floquet systems in even spatial dimensions.