Results 1  10
of
43
Emergent Gravity from Noncommutative Gauge Theory
, 2007
"... We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dyn ..."
Abstract

Cited by 60 (29 self)
 Add to MetaCart
We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.
Induced gauge theory on a noncommutative space.
 Zbl 1189.81217 MR
, 2007
"... We discuss the calculation of the 1loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar φ 4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge fiel ..."
Abstract

Cited by 52 (16 self)
 Add to MetaCart
We discuss the calculation of the 1loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar φ 4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model.
Heat Kernel and Number Theory on NCTorus
 Commun. Math. Phys
, 2007
"... The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the numbertheoretical aspect of the deformation parameters. The central condition we ..."
Abstract

Cited by 17 (10 self)
 Add to MetaCart
(Show Context)
The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the numbertheoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find nonlocal counterterms in the NC φ 4 theory on T 4, we show that this theory can be made renormalizable at least at one loop, and may be even beyond.
Noncommutative QFT and Renormalization
, 2006
"... Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to φ 3 models and use the heat kernel ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to φ 3 models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θdeformed space and derive noncommutative gauge field actions.
The spectral distance in the Moyal plane
, 2011
"... We study the noncommutative geometry of the Moyal plane from a metric point of view. Starting from a non compact spectral triple based on the Moyal deformation A of the algebra of Schwartz functions on R2, we explicitly compute Connes ’ spectral distance between the pure states of A corresponding to ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
We study the noncommutative geometry of the Moyal plane from a metric point of view. Starting from a non compact spectral triple based on the Moyal deformation A of the algebra of Schwartz functions on R2, we explicitly compute Connes ’ spectral distance between the pure states of A corresponding to eigenfunctions of the quantum harmonic oscillator. For other pure states, we provide a lower bound to the spectral distance, and show that the latest is not always finite. As a consequence, we show that the spectral triple [19] is not a spectral metric space in the sense of [5]. This motivates the study of truncations of the spectral triple, based on Mn(C) with arbitrary n ∈ N, which turn out to be compact quantum metric spaces in the sense of Rieffel. Finally the distance is explicitly computed for n = 2.
Noncompact spectral triples with finite volume
"... Abstract. In order to extend the spectral action principle to noncompact spaces, we propose a framework for spectral triples where the algebra may be nonunital but the resolvent of the Dirac operator remains compact. We show that an example is given by the supersymmetric harmonic oscillator which, ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In order to extend the spectral action principle to noncompact spaces, we propose a framework for spectral triples where the algebra may be nonunital but the resolvent of the Dirac operator remains compact. We show that an example is given by the supersymmetric harmonic oscillator which, interestingly, provides two different Dirac operators. This leads to two different representations of the volume form in the Hilbert space, and only their product is the grading operator. The index of the eventoodd part of each of these Dirac operators is 1. We also compute the spectral action for the corresponding ConnesLott twopoint model. There is an additional harmonic oscillator potential for the Higgs field, whereas the YangMills part is unchanged. The total Higgs potential shows a twophase structure with smooth transition between them: In the spontaneously broken phase below a critical radius, all fields are massive, with the Higgs field mass slightly smaller than the NCG prediction. In the unbroken phase above the critical radius, gauge fields and fermions are massless, whereas the Higgs field remains massive. 1.
Particle Physics from AlmostCommutative Spacetimes
, 2014
"... Our aim in this review article is to present the applications of Connes’ noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physi ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
Our aim in this review article is to present the applications of Connes’ noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists’ terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (socalled ‘almostcommutative manifolds’), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein’s (geometrical) theory of gravity.