Related papers: Generalized Higher Gauge Theory
We discuss a generalization of Chern-Simons theory in three dimensions based on Leibniz (or Loday) algebras, which are generalizations of Lie algebras. Special cases of such theories appear in gauged supergravity, where the Leibniz algebra…
In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of $4$d Chern-Simons theory with defects, which provided a…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…
We undertake a detailed study of the gaugings of two-dimensional Yang-Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes…
The focus of these lectures is the Gopakumar-Vafa's insight that ``Large N dualities'' (relating gauge theories and closed strings) are realized, in certain cases, by "transition in geometry". In their pivotal 1998 example, the gauge theory…
Contact terms in two point functions of global symmetry currents have recently been proposed as a check of Seiberg-like duality in three dimensional supersymmetric field theories. In this paper we compute the contact terms for various N=2…
We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
It is well-known that if we gauge a $\mathbb{Z}_n$ symmetry in two dimensions, a dual $\mathbb{Z}_n$ symmetry appears, such that re-gauging this dual $\mathbb{Z}_n$ symmetry leads back to the original theory. We describe how this can be…
A framework for higher gauge theory based on a 2-group is presented, by constructing a groupoid of connections on a manifold acted on by a 2-group of gauge transformations, following previous work by the authors where the general notion of…
Motivated by some previously known facts from mathematical and physics literature, we explore certain relations between 3-dimensional topological gauge theories with continuous and finite gauge groups, commonly known as Chern-Simons (CS)…