We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form to form continuous 2-group. All these models can be obtained by performing gauging procedure in parent theory revealing 't Hooft anomaly the space coupling constants when suitable compact scalar background fields are activated. Furthermore, also implies that our main example has ...

We study generalized symmetries in a simplified arena which the usual quantum field theories of physics are replaced with topological and smooth structure symmetry groups usually endowed is forgotten. Doing so allows many questions physical interest to be answered using tools homotopy theory. both global gauge symmetries, as well `t Hooft anomalies, we show fall into one two classes. Our approa...

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, i.e., at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point...

We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous. Such higher-form global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a non-conformal field theory with a ...

We define the notion of amomentmap and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on CP , Hirzebruch surfaces, the blow up of CP at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher-rank Z Anosov actions on T and the classification of equilibrium-free flows on T that possess nontrivial generalized symmetries.