Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions

TL;DR

This paper develops a lattice framework for studying topological gauging interfaces, defects, and anomalies in higher-dimensional systems with generalized symmetries, providing explicit constructions and analysis methods.

Contribution

It introduces movement operators to handle interface constraints, constructs explicit Hamiltonians for gauging symmetries in higher dimensions, and analyzes anomalies via condensation defects.

Findings

Constructed explicit interface Hamiltonians for higher-dimensional gauging.

Introduced movement operators to manage interface constraints.

Analyzed anomalies through symmetry fractionalization on condensation defects.

Abstract

We study gauging interfaces and their defect descendants in lattice models with generalized symmetries in higher dimensions. We construct explicit interface Hamiltonians for gauging a $\mathbb Z_2^{(0)}$ symmetry in $(2+1)d$ and a $\mathbb Z_2^{(1)}$ symmetry in $(3+1)d$. In higher dimensions, and especially in the presence of higher-form symmetries, the topological nature of gauging interfaces is obscured by the fact that the constrained Hilbert space depends on the location of the interface. We resolve this by introducing movement operators acting on a common unconstrained Hilbert space, which transport both the interface Hamiltonians and the associated constraints. As applications, we analyze condensation defects obtained from finite-region gauging and reconstruct the gauging map from movement operators. Finally, we apply the same framework to subgroup gauging, focusing on the example of gauging $\mathbb Z_2\subset \mathbb Z_4$. This produces a dual symmetry carrying a mixed anomaly, which we diagnose on the lattice through symmetry fractionalization on condensation defects. Our results provide an explicit lattice framework for studying topological interfaces, condensation defects, and the associated anomalies arising from gauging in higher-dimensional systems.