Field equations of massless fields in the new interpretation of the matrix model

Furuta, Ko; Hanada, Masanori; Kawai, Hiroyuki; Kimura, Yusuke

doi:10.1016/j.nuclphysb.2007.01.003

Cited by 28 publications

(30 citation statements)

References 17 publications

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“…Alternatively, one can use another type of noncommutative geometries, matrix geometries, in order to explore quantum gravity. [19,20] Several approaches have been suggested in recent years, mainly based on Yang-Mills matrix models, [21][22][23][24][25][26][27][28][29][30][31] pointing once more at direct relations among noncommutative gauge theories and gravity. For another approach see Refs.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative Gauge Theory and Gravity in Three Dimensions

Chatzistavrakidis

Jonke

Jurman

et al. 2018

Fortschritte der Physik

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The Einstein-Hilbert action in three dimensions and the transformation rules for the dreibein and spin connection can be naturally described in terms of gauge theory. In this spirit, we use covariant coordinates in noncommutative gauge theory in order to describe 3D gravity in the framework of noncommutative geometry. We consider 3D noncommutative spaces based on SU(2) and SU(1,1), as foliations of fuzzy 2-spheres and fuzzy 2-hyperboloids respectively. Then we construct a U(2) × U(2) and a GL(2,C) gauge theory on them, identifying the corresponding noncommutative vielbein and spin connection. We determine the transformations of the fields and an action in terms of a matrix model and discuss its relation to 3D gravity.1 This is also true in any dimension for what concerns the transformation rules of the fields. 2 We employ the standard convention that antisymmetrizations are taken with weight 1.

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Section: Introductionmentioning

confidence: 99%

Noncommutative Gauge Theory and Gravity in Three Dimensions

Chatzistavrakidis

Jonke

Jurman

et al. 2018

Fortschritte der Physik

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“…Then, some components of the torsion field 53) can be identified with the matter fields in type II string theories, that is, in the bosonic sector, the dilaton field and the B-fields. [127] Here, all of the local fields are unified in each loop algebra component of the generalized Utiyama fields with torsion a * µ (s µ ), which is considered to represent the T-dual description of the field of clusters of D-strings, and are distinguished by their geometrical roles in a * µ (s µ ). This distinguishability is compatible with the loop algebra structure of the gauge potentials a * µ (s µ ), as remarked before, just as it is in the context of type IIB matrix model.…”

Section: T-dual Representation Of the Field Variablesmentioning

confidence: 99%

Time and a Temporally Statistical Quantum Geometrodynamics

Konishi

2013

Int. J. Mod. Phys. A

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This paper is an exposition of the author's recent work on modeling M-theory vacua and quantum mechanical observers in the framework of a temporally statistical description of quantum geometrodynamics, including measurement processes based on the canonical theory of quantum gravity. In this paper we deal with several fundamental issues of time:the time-less problem in canonical quantum gravity; the physical origin of state reductions; and time-reversal symmetry breaking. We first model the observers and consider the timeless problem by invoking the time reparametrization symmetry breaking in the quantum mechanical world as seen by the observers. We next construct the hidden time variable theory, using a model of the gauged and affinized S-duality symmetry in type IIB string theory, as the statistical theory of time and explain the physical origin of state reductions using it. Finally, by the extension of the time reparametrization symmetry to all of the temporal hidden variables, we treat the issue of time reversal symmetry breaking as the spontaneous breaking of this extended time reparametrization symmetry. The classification of unitary time-dependent processes and the geometrizations of unitary and non-unitary time evolutions using the language of the derived category are also investigated.

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“…Several approaches have been suggested, mainly based on Yang-Mills matrix models [20][21][22][23][24][25][26][27][28][29][30], pointing once more at direct relations among noncommutative gauge theories and gravity. For another approach see Refs.…”

Section: Introductionmentioning

confidence: 99%

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Jurman¹,

Manolakos²,

Manousselis³

et al. 2018

Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)

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We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2) and SU(1,1), which carry appropriate symmetry groups. These are the groups we are going to gauge in order to result with the transformations of the gauge fields (dreibein, spin connection and two extra Maxwell fields due to noncommutativity), their corresponding curvatures and eventually determine the action and the equations of motion. Finally, we verify their connection to three-dimensional gravity.

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Field equations of massless fields in the new interpretation of the matrix model

Cited by 28 publications

References 17 publications

Noncommutative Gauge Theory and Gravity in Three Dimensions

Noncommutative Gauge Theory and Gravity in Three Dimensions

Time and a Temporally Statistical Quantum Geometrodynamics

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

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