Continuous Generalized Symmetries in Three Dimensions

TL;DR

This work develops a framework for continuous $2$-group global symmetries in three dimensions by gauging compact scalar backgrounds, thereby mixing 0-form and 1-form symmetries through anomaly in the space of couplings. It provides explicit 3d constructions—Goldstone, Goldstone–Maxwell, and Goldstone–Yang–Mills—and connects them via dimensional reduction from 4d, while revealing infinite families of non-invertible symmetry defects in the GM model that arise from dressing symmetry operators with topological sectors. A complementary holographic dictionary in AdS$_4$ ties the boundary $2$-group and non-invertible structures to bulk dynamical gauge fields and inflow, including Green–Schwarz couplings and boundary condition exchanges. The results illuminate how generalized global symmetries can be organized in 3d QFTs, with potential implications for holography and non-invertible symmetry phenomena. Overall, the paper shows that continuous higher-group symmetries and non-invertible defects can be realized coherently in low-dimensional quantum field theories and their holographic duals.

Abstract

We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a 't Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields.