Continuous generalized symmetries in three dimensions

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.

Automated summary

We propose a class of 3D quantum field theories where ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. These models can be obtained by gauging a parent theory and activating suitable compact scalar background fields, which reveal a 't Hooft anomaly in the space of coupling constants. Moreover, the gauging procedure implies that our main example has infinitely many non-invertible global symmetries, which can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we discuss the holographic realization of these 2-group global symmetries and non-invertible symmetries by introducing a corresponding four-dimensional bulk description with dynamical gauge fields.