Fermions and noncommutative emergent gravity II: curved branes in extra dimensions

Klammer, Daniela; Steinacker, Harold

doi:10.1007/jhep02(2010)074

Cited by 7 publications

(17 citation statements)

References 25 publications

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Order By: Relevance

“…[11]. This is consistent with the semi-classical result in [21], but the present derivation is exact to all orders in θ. Higher-order terms in the expansion (4.30) will contribute in particular to the curvature action.…”

Section: Order By Order Computationssupporting

confidence: 92%

“…However, there are also terms such as TrL 10,C ∼ 1 (2π) 2 d 4 x √ g X a g X a which correspond to extrinsic curvature on M ⊂ R D . The structure is consistent with the semiclassical results obtained in [21], and a more precise result should be given once the remaining coefficients for L cubic are known.…”

Section: Effective Matrix Model Including Curvature Contributionssupporting

confidence: 86%

“…Note that this term is comparable with the Λ 2 contribution if Λ ≈ Λ NC , but is negligible if Λ ≪ Λ NC . It is also worth pointing out that this contribution may not be obtained in a semi-classical analysis along the lines of [20,21], because it involves a higher-order contribution in the UV/IR mixing term (5.10).…”

Section: O(λ 6 ) Curvature Termsmentioning

confidence: 99%

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Heat kernel expansion and induced action for the matrix model Dirac operator

Blaschke

Steinacker

Wohlgenannt

2011

J. High Energ. Phys.

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We compute the quantum effective action induced by integrating out fermions in Yang-Mills matrix models on a 4-dimensional background, expanded in powers of a gauge-invariant UV cutoff. The resulting action is recast into the form of generalized matrix models, manifestly preserving the SO(D) symmetry of the bare action. This provides non-commutative (NC) analogs of the Seeley-de Witt coefficients for the emergent gravity which arises on NC branes, such as curvature terms. From the gauge theory point of view, this provides strong evidence that the non-commutative N = 4 SYM has a hidden SO(10) symmetry even at the quantum level, which is spontaneously broken by the space-time background. The geometrical view proves to be very powerful, and allows to predict non-trivial loop computations in the gauge theory.

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Section: Order By Order Computationssupporting

confidence: 92%

Section: Effective Matrix Model Including Curvature Contributionssupporting

confidence: 86%

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Heat kernel expansion and induced action for the matrix model Dirac operator

Blaschke

Steinacker

Wohlgenannt

2011

J. High Energ. Phys.

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“…There is in fact a way to formally obtain the full vacuum Einstein equations[21], which however leads to other issues 3. This would not be possible on simple noncommutative spaces such as R 4 n , where extra terms are possible which are forbidden here[45]. This is very important for obtaining a realistic physics.…”

mentioning

confidence: 99%

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Sperling¹,

Steinacker²

2019

J. High Energ. Phys.

101

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We discuss a (3+1)-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid H 4 n . This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higherspin modes, truncated at n. The modes are organized in terms of an underlying SO(4, 2) structure group, which is broken to the SO(3, 1) isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.12 Note that SO(4, 2) should not be interpreted as conformal group on H 4 , rather it provides the organization of the higher-spin modes on H 4 and M 3,1 . 13 We will ignore the dependence on two sheets M ± for simplicity.

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“…which should also appear, as was discussed in [1,9,25,26]. These would then be higher-order commutator terms, as indicated by "h.o."…”

Section: Fermion Induced Actionmentioning

confidence: 86%

Heat kernel expansion and induced action for matrix models

Blaschke

2012

J. Phys.: Conf. Ser.

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In this proceeding note 1 , 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. BackgroundOne of the greatest challenges of present day physics is to find a mathematical framework to describe quantum field theory formulated on some quantum space-time. This would be necessary in order to combine the standard model of particle physics with gravity. Surely, many ideas are currently around and it remains unclear which is the best way to achieve this goal. What I would like to present in this short proceeding note, are some recent results [1,2] which are based on the idea of gravity as an emergent force derived from matrix models -for a general introduction to the subject, the interested reader is referred to [3].It is indeed not easy to find a new model that is renormalizable, but a concept that is known to greatly improve the properties of a model with respect to divergences and renormalizability is supersymmetry. Incidentally, a supersymmetric matrix model which turns out to achieve what we want, namely incorporating scalars, fermions, gauge bosons and (emergent) gravity was originally introduced as a non-perturbative description of type IIB string theory: It is the so-called IKKT model, named after its authors [4], and given by the actionwhere X a , a = 0, 1, 2, . . . , 9 are Hermitian matrices, Ψ is a matrix-valued Majorana-Weyl spinor of SO(9, 1), and the γ a form the corresponding Clifford algebra. The model is obtained by dimensional reduction of the 10-dimensional SU (N ) Super-Yang-Mills theory to a point, and * daniel.blaschke@univie.ac.at 1 based on a talk given at the 7 th International Conference on Quantum Theory and Symmetries, August 7-13, 2011 in Prague, Czech Republic 1 arXiv:1111.0876v1 [hep-th] 3 Nov 2011 taking the N → ∞ limit. Indices are raised and lowered using the fixed background metric g ab , which we consider to either be the ten-dimensional Minkowski or Euclidean metric. The action (1) is invariant under the N = 2 matrix supersymmetryas well as the additional symmetrieswhere the tilde indicates the corresponding spin group. Although an explicit proof to all orders is still missing, there are good reasons to believe that this model is in fact renormalizable [4,5].Here we take the IKKT matrix model model (1) as a starting point independent of string theory, and focus on 4-dimensional brane solutions or backgrounds, considered as physical space(-time). Due to supersymmetry, the model should provide a well-defined quantum theory at least for 4-dimensional backgrounds. In fact, numerical evidence for the emergence of 3+1-dimensional space-time within the IKKT model has been obtained recently in Ref. [6], providing further motivation to study the effective physics of 4-dimensional backgrounds.Additionally, it was shown in [7] ho...

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Fermions and noncommutative emergent gravity II: curved branes in extra dimensions

Cited by 7 publications

References 25 publications

Heat kernel expansion and induced action for the matrix model Dirac operator

Heat kernel expansion and induced action for the matrix model Dirac operator

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Heat kernel expansion and induced action for matrix models

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