Related papers: Finite-dimensional algebras, gauge-string duality …
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
The matrix model computations of effective superpotential terms in N=1 supersymmetric gauge theories in four dimensions have been proposed to apply more generally to gauge theories in higher dimensions. We discuss aspects of…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each…
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition.…
We review some recent results on phenomenological approaches to strong interactions inspired in gauge/string duality. In particular, we discuss how such models lead to very good estimates for hadronic masses.
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way.…
According to the gauge/gravity duality conjecture, the thermodynamics of gauge theory describing D-branes corresponds to that of black branes in superstring theory. We test this conjecture directly in the case of D0-branes by applying Monte…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
In this thesis we will study matrix models with discrete gauge group $S_N$. We will put these matrix models into a generalized Schur-Weyl duality framework where dual algebras, known as partition algebras, emerge. These form generalizations…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity…
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of…