Related papers: Double groupoids in the theory of material uniform…
We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries.…
We study various cases of dualities between $\cal{N}$$=1$ 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the…
This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects…
We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
2-group symmetries arise in physics when a 0-form symmetry $G^{[0]}$ and a 1-form symmetry $H^{[1]}$ intertwine, forming a generalised group-like structure. Specialising to the case where both $G^{[0]}$ and $H^{[1]}$ are compact, connected,…
The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher…
Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Mackenzie; in particular, we…
Four dimensional N=1 supersymmetric gauge theories with unitary gauge groups and matter in the adjoint and fundamental representations give rise to a series of non-trivial fixed points with an ADE classification. Many of these models…
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…
In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…
In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.
A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are…
The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie…
We introduce the notion of G-algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in $E_{n(n)}\times\mathbb{R}^+$ exceptional generalised geometry for $n\in\{3,\dots,6\}$. Focusing on the exceptional case,…
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…