Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

Aschieri, Paolo; Grammatikopoulos, Theodoros; Steinacker, Harold; Zoupanos, George

doi:10.1088/1126-6708/2006/09/026

Cited by 92 publications

(229 citation statements)

References 28 publications

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“…up to epochs with TeV-range temperature in the case of TeV-scale supersymmetry. Some modifications could arise from compactification in extra dimensions (leading to interesting low-energy gauge groups, effective scalar fields & potentials as in [12]), or soft SUSY breaking terms (e.g. a mass term) in the matrix model.…”

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confidence: 99%

Cosmological Solutions of Emergent Noncommutative Gravity

Klammer

Steinacker

2009

Phys. Rev. Lett.

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Matrix models of Yang-Mills type lead to an emergent gravity theory, which may not require fine-tuning of a cosmological constant. We find cosmological solutions of Friedmann-RobertsonWalker type. They generically have a big bounce, and an early inflation-like phase with graceful exit. The mechanism is purely geometrical, no ad-hoc scalar fields are introduced. The solutions are stabilized through vacuum fluctuations and are thus compatible with quantum mechanics. This leads to a Milne-like universe after inflation, which appears to be in remarkably good agreement with observation and may provide an alternative to standard cosmology.PACS numbers: 98.80.Qc, 98.80.Cq Quantum field theory and general relativity provide the basis of our present understanding of fundamental forces and matter. However, there is up to now no satisfactory way to reconcile them in a consistent quantum theory. General arguments based on quantum mechanics and general relativity suggest a "foam-like" or quantum structure at the Planck scale 10 −33 cm. This problem has its most dramatic manifestation in the cosmological constant problem: the small but non-vanishing cosmological constant in the currently accepted ΛCDM model is in striking contradiction with quantum mechanical expectations, which are off by at least 60 orders of magnitude. No satisfactory solution of this problem within the conventional frameworks has been found.We point out in this letter that emergent gravity on non-commutative (NC) spaces may provide a resolution of these problems. The starting point are matrix models of Yang-Mills typesupplemented by suitable fermionic terms. Such models have been discussed in the context of NC gauge theory and string theory. Here X a , a = 1, ..., D are (infinite-dimensional) hermitian matrices, and η ab = diag(1, 1, ..., ±1) in the Euclidean resp. Minkowski case. The basic hypothesis of our approach is that space-time is realized as 3+1-dimensional NC "brane" solution of such a model. The effective geometry and gravity on such a brane was clarified recently [1][2][3]: the effective metric is not fundamental but depends on the embedding and the Poisson structure, reminiscent of the open string metric [7]. This leads to an emergent gravity closely related to NC gauge theory, as anticipated in [5,6]. Among these models, the IKKT model [8] is singled out by maximal supersymmetry, required by consistency at the quantum level. This implies in particular D = 10, which we assume from now on. This model is a candidate for a theory of all fundamental interactions and matter. * Electronic address: daniela.klammer@univie.ac.at † Electronic address: harold.steinacker@univie.ac.atThe model admits 4-dimensional noncommutative spaces M θ ⊂ R 10 as solution, interpreted as space-time embedded in 10 dimensions. This can be seen by splitting the matrices aswhere the "scalar fields" φ i = φ i (X µ ) are assumed to be functions of X µ . We only consider the semi-classical limit of such a quantum space, indicated by ∼. Then X µ ∼ x µ is interpreted as qua...

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confidence: 99%

Cosmological Solutions of Emergent Noncommutative Gravity

Klammer

Steinacker

2009

Phys. Rev. Lett.

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“…Next we reverse the above approach [68] and examine how a four dimensional gauge theory dynamically develops higher dimensions. The very concept of dimension therefore gets an extra, richer dynamical perspective.…”

Section: Unif Ied Theories From Fuzzy Higher Dimensionsmentioning

confidence: 99%

“…Let us now discuss a further development [68] of these ideas, which addresses in detail the questions of quantization and renormalization. This leads to a slightly modified model with an extra term in the potential, which dynamically selects a unique (nontrivial) vacuum out of the many possible CSDR solutions, and moreover generates a magnetic flux on the fuzzy sphere.…”

Section: Dynamical Generation Of Extra Dimensionsmentioning

confidence: 99%

Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

Mondragón

Zoupanos

2008

SIGMA

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Abstract. Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized a la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU (N ) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere S 2 N . We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M 4 × S 2 , the scalars being interpreted as gauge fields on S 2 . Depending on the parameters of the model the low-energy gauge group can be SU (n), or broken further to SU (n 1 ) × SU (n 2 ) × U (1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory.

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“…Finally, I would like to point out a realization of the ideas and results of section 3 within the context of ordinary, renormalizable 4-dimensional gauge theory [21]. We start with a SU (N ) gauge theory on 4-dimensional Minkowski space M 4 , and add 3 antihermitian scalar fields with the most general renormalizable action invariant under an additional global SU (2) symmetry.…”

Section: Fuzzy Extra Dimensionsmentioning

confidence: 99%

“…The appropriate interpretation is then as an U (n) gauge theory on M 4 × S 2 . The details of this will be published elsewhere [21].…”

Section: Fuzzy Extra Dimensionsmentioning

confidence: 99%