Related papers: On the Composition of Gauge Structures
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
Some very simple models of gauge systems with noncanonical symplectic structures having $sl(2,r)$ as the gauge algebra are given. The models can be interpreted as noncommutative versions of the usual $SL(2,\mathbb{R})$ model of…
We describe how a soft supersymmetry breaking Lagrangian arises naturally in the context of almost-commutative geometries that fall within the classification of those having a supersymmetric particle content as well as a supersymmetric…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
The supergravity dual of superconformal anomaly in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between the ${\cal N}=1$ $SU(N+M)\times SU(N)$ supersymmetric gauge theory…
Two main themes populate this Thesis's pages: transgression forms as Lagrangians for gauge theories and the Abelian semigroup expansion of Lie algebras. A transgression form is a function of two gauge connections whose main property is its…
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
One of the biggest challenges to theoretical physics of our time is to find a background-independent quantum theory of gravity. Today one encounters a profusion of different attempts at quantization, but no fully accepted - or acceptable,…
It is shown that the super Higgs mechanism that occurs in a wide class of models with vanishing cosmological constant (at the classical level) is obtained by the gauging of a flat group which must be an electric subgroup of the duality…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
We find a dual gravity theory to pure confining N=1 supersymmetric SU(N) gauge theory in four dimensions which has the correct gauge coupling running in addition to reproducing the appropriate pattern of chiral symmetry breaking. It is…
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two…
Starting from flat two-dimensional gauge potentials we propose the notion of ${\cal W}$-gauge structure in terms of a nilpotent BRS differential algebra. The decomposition of the underlying Lie algebra with respect to an $SL(2)$ subalgebra…
Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra…
A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular…
We present a short overview of the structure and couplings of supergravity theories at the component level. We do so with as little technical machinery as possible, working directly with the physical on-shell fields and using explicit…