Emergent gravity from noncommutative gauge theory

Steinacker, Harold

doi:10.1088/1126-6708/2007/12/049

Cited by 128 publications

(231 citation statements)

References 63 publications

(139 reference statements)

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“…It was observed that a massless scalar and vector fields coupled to NC U (1) gauge field, after the SW mapping, has the same structure as that of fields coupled with gravity [8]. This suggestion, that gravity can emerge from NC electromagnetism, has been further studied and extended in [9,10]. Hence it is natural to ask whether the 2-form field coupled to photons in NC space-time has such an emergent gravity coupling.…”

Section: Introductionmentioning

confidence: 99%

Aspects of a noncommutative scalar/tensor duality

et al. 2008

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We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U (1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in θ. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order θ is also derived.

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Section: Introductionmentioning

confidence: 99%

Aspects of a noncommutative scalar/tensor duality

et al. 2008

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“…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].…”

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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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“…(2.11). 4 for massless particles, the geodesics ofG ab coincide with those of G ab . Masses should be generated spontaneously, which is not considered here.…”

Section: Quantization and Induced Gravitymentioning

confidence: 91%

“…Then the conventional kinetic term (2.13) boils down to (2.11). Therefore in the point-particle limit, the trajectory of a fermion with action (2.11) will follow properly the geodesics of the metric 4 G ab , albeit with a different rotation of the spin. Furthermore, the induced gravitational action obtained by integrating out the fermion in (2.11) indeed induces the expected Einstein-Hilbert term…”

Section: Matrix Models and Effective Geometrymentioning

confidence: 99%

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Emergent noncommutative gravity

Klammer¹

2009

Proceedings of Black Holes in General Relativity and String Theory — PoS(BHs, GR and Strings)

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We study the coupling of fermions to Yang-Mills matrix models in the framework of emergent noncommutative gravity. It is shown that the matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin-connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action for on-shell geometries plus a dilaton-like term. This result explains UV/IR mixing as a gravity effect. It also illuminates why UV/IR mixing remains even in supersymmetric models, except in the N = 4 case.

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Emergent gravity from noncommutative gauge theory

Cited by 128 publications

References 63 publications

Aspects of a noncommutative scalar/tensor duality

Aspects of a noncommutative scalar/tensor duality

Cosmological Solutions of Emergent Noncommutative Gravity

Emergent noncommutative gravity

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