Higher-Form Response of 3D Fractional Topological Insulators

Three-dimensional fractional topological insulators (FTIs) are exotic symmetry enriched phases hosting extended defects with anyonic statistics. Here we consider the higher-form global symmetries and anomalies of a special family of bulk FTI models based on Z_N lattice gauge theory with a fractional theta term, which were originally explored by Cardy and Rabinovici. These models host dyon excitations that condense to form the FTI phase. We examine the 't Hooft anomalies and response of these theories to an external two-form gauge field that probes their electric Z_N one-form symmetry, which we show leads to a universal topological index for the FTI state.