Related papers: Symmetry, Gravity and Noncommutativity
We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…
The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure…
We give a pedagogical introduction to $L_\infty$-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective…
We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional…
In string theory, D-branes can be expressed as a configuration of infinitely many lower dimensional D-branes. Using this relation, the worldvolume theory of D-branes can be regarded as the worldvolume theory of the infinitely many lower…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
We construct noncommutative gauge theories based on the notion of the Weyl bundle, which appears in Fedosov's construction of deformation quantization on an arbitrary symplectic manifold. These correspond to D-brane worldvolume theories in…
Spacetime non-commutativity appears in string theory. In this paper, the non-commutativity in string theory is reviewed. At first we review that a Dp-brane is equivalent to a configuration of infinitely many D($p-2$)-branes. If we consider…
This report presents some studies of the gauge/string theory correspondence, a deep relation that is possible to establish between quantum field theories with local gauge symmetry and superstring theories including gravity. In its original…
We study a class of noncommutative geometries that give rise to dimensionally reduced Yang-Mills theories. The emerging geometries describe sets of copies of an even dimensional manifold. Similarities to the D-branes in string theory are…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We construct twisted noncommutative gauge theories on twistor space and show that they are equivalent to four-dimensional twist-noncommutative gauge theories. In particular, we study twists of the Poincar\'e algebra. We explain how such a…
The great deal in noncommutative (NC) field theories started when it was noted that NC spaces naturally arise in string theory with a constant background magnetic field in the presence of $D$-branes. Besides their origin in string theories…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups,…
We discuss the supergravity couplings of noncommutative D-branes by considering the disk amplitudes with one closed string insertion. The result confirms a recent proposal for the general form of the noncommutative Yang-Mills operators…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…