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33
Covariant Field Equations, Gauge Fields and Conservation Laws from YangMills Matrix Models
, 2008
"... The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in YangMills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as YangMills algebra. Remarkably, the equations of moti ..."
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Cited by 20 (17 self)
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The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in YangMills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as YangMills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the wouldbe topological term. In particular, the IKKT matrix model is capable of describing 4dimensional NC spacetimes with a general effective metric. Metric deformations of flat MoyalWeyl space are briefly discussed.
On the Newtonian limit of emergent NC gravity and longdistance corrections
, 2009
"... We show how Newtonian gravity emerges on 4dimensional noncommutative spacetime branes in YangMills matrix models. Large matter clusters such as galaxies are embedded in largescale harmonic deformations of the spacetime brane, which screen gravity for long distances. On shorter scales, the local ..."
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Cited by 10 (9 self)
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We show how Newtonian gravity emerges on 4dimensional noncommutative spacetime branes in YangMills matrix models. Large matter clusters such as galaxies are embedded in largescale harmonic deformations of the spacetime brane, which screen gravity for long distances. On shorter scales, the local matter distribution reproduces Newtonian gravity via local deformations of the brane and its metric. The harmonic “gravity bag ” acts as a halo with effective positive energy density. This leads in particular to a significant enhancement of the orbital velocities around galaxies at large distances compared with the Newtonian case, before dropping to zero as the geometry merges with a Milnelike cosmology. Besides these “harmonic ” solutions, there is another class of solutions which is more similar to Einstein gravity. Thus the IKKT model provides an accessible candidate for a quantum theory of gravity.
Fermions and noncommutative emergent gravity. II. Curved branes in extra dimensions
 J. High Energy Phys
"... branes in extra dimensions ..."
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PROJECTIVE MODULE DESCRIPTION OF EMBEDDED NONCOMMUTATIVE SPACES
, 810
"... ABSTRACT. Noncommutative differential geometry over the Moyal algebra is developed following an algebraic approach. It is then applied to investigate embedded noncommutative spaces. We explicitly construct the projective modules corresponding to the tangent bundles of the noncommutative spaces, and ..."
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Cited by 5 (3 self)
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ABSTRACT. Noncommutative differential geometry over the Moyal algebra is developed following an algebraic approach. It is then applied to investigate embedded noncommutative spaces. We explicitly construct the projective modules corresponding to the tangent bundles of the noncommutative spaces, and recover from this algebraic formulation the metric, LeviCivita connection and related curvature introduced in earlier work. Transformation rules of connections and curvatures under general coordinate changes are given explicitly. A bar involution on the Moyal algebra is discovered, and its consequences on the noncommutative differential geometry are described. CONTENTS
Heat kernel expansion and induced action for matrix models
, 2011
"... In this proceeding note1, I review some recent results concerning the quantum effective action of certain matrix models, i.e. the supersymmetric IKKT model, in the context of emergent gravity. The absence of pathological UV/IR mixing is discussed, as well as dynamical SUSY breaking and some relation ..."
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Cited by 4 (3 self)
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In this proceeding note1, I review some recent results concerning the quantum effective action of certain matrix models, i.e. the supersymmetric IKKT model, in the context of emergent gravity. The absence of pathological UV/IR mixing is discussed, as well as dynamical SUSY breaking and some relations with string theory and supergravity. 1
Gauge Theories on Deformed Spaces
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2010
"... The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common fe ..."
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The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.
Generalized Fuzzy Torus and its Modular Properties ⋆
"... Abstract. We consider a generalization of the basic fuzzy torus to a fuzzy torus with nontrivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semiclassical limit, the generali ..."
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Abstract. We consider a generalization of the basic fuzzy torus to a fuzzy torus with nontrivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semiclassical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed. Key words: fuzzy spaces; noncommutative geometry; matrix models 2010 Mathematics Subject Classification: 81R60; 81T75; 81T30 1
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
"... Over the past decades, noncommutative geometry has grown into an established field in pure mathematics and theoretical physics. The discovery that noncommutative geometry emerges as a limit of quantum gravity and string theory has provided strong motivations to search for physics beyond the standard ..."
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Over the past decades, noncommutative geometry has grown into an established field in pure mathematics and theoretical physics. The discovery that noncommutative geometry emerges as a limit of quantum gravity and string theory has provided strong motivations to search for physics beyond the standard model of particle physics and also beyond Einstein’s theory of general relativity within the realm of noncommutative geometries. A very fruitful approach in the latter direction is due to Julius Wess and his group, which combines deformation quantization (?products) with quantum group methods. The resulting gravity theory does not only include noncommutative effects of spacetime, but it is also invariant under a deformed Hopf algebra of diffeomorphisms, generalizing the principle of general covariance to the noncommutative setting. The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. These are important investigations in order to capture the physical content of such theories and to make contact to applications in e.g. noncommutative cosmology and black hole physics. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein’s field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of