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The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by $G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\ with vector gauge couplings) are in the adjoint representation of the subgroup $H \subset…
We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a…
We discuss new-type grand unified theories based on grand unified groups broken to their special subgroups as well as their regular subgroups. In the framework, when we construct four-dimensional (4D) chiral gauge theories, i.e., the…
We discuss how electromagnetically dualizing a 1-form to a 2-form in AdS$_5$ exchanges regular and alternate boundary conditions, and thus gauges the originally global $U(1)$ symmetry in the dual field theory. The generalized symmetry…
Standard lore views our 4d quantum vacuum governed by one of the candidate Standard Models (SMs), while lifting towards some Grand Unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
Dirac fermion fields are responsible for spontaneous symmetry breaking in gauge gravitation theory because the spin structure associated with a tetrad field is not preserved under general covariant transformations. Two solutions of this…
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant…
We study discrete symmetries of Dijkgraaf-Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete…
We introduce a new version of non-linear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the non-zero expectation value of the electromagnetic field strength. The symmetry breaking…
The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1- and 2-forms. So far, there have been two approaches to this subject. The differential picture uses…
Starting with a choice of gauge algebras, specification of a 4d gauge theory involves additional data, namely the gauge groups and the discrete theta angles. Equivalently, one needs to specify the set of charges of allowed line operators.…
We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a $U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$. We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for $N>2$.…
We consider localized anomalies in six dimensional Z_n orbifolds. We give a very simple expression for the contribution of a bulk fermion to the fixed point gauge anomaly that is independent of the order n of the orbifold twist. We show it…
We discuss a grand unified theory (GUT) based on an $SO(32)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SO(32)$ GUT on six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$, one generation of…
Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This…
A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy $W$-symmetry of Howe and Papadopoulos associated with…
An extended field theory is presented that captures the full SL(2) x O(6,6+n) duality group of four-dimensional half-maximal supergravities. The theory has section constraints whose two inequivalent solutions correspond to minimal D=10…
We consider the topological gauged WZW model in the generalized momentum representation. The chiral field $g$ is interpreted as a counterpart of the electric field $E$ of conventional gauge theories. The gauge dependence of wave functionals…
For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\mathcal A$, with a non-trivial center $\mathcal Z$, describes observables, the other Weyl…