Seiberg-Witten maps for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>gauge invariance and deformations of gravity

Mǎrculescu, S.; Ruiz, F. Ruiz

doi:10.1103/physrevd.79.025004

Cited by 16 publications

(17 citation statements)

References 36 publications

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“…General relativity on noncommutative spacetime has also been constructed by gauging the twist-deformed Poincaré symmetry [72]. Deformations of gravity can moreover be induced from a noncommutative gauge theory with position-dependent noncommutativity θ µν (x) using the Seiberg-Witten map [73]. We will shortly see how an analogous procedure can be used to extract general relativity more precisely from the dynamics of noncommutative gauge fields.…”

Section: Gravity In Noncommutative Gauge Theoriesmentioning

confidence: 98%

Quantum gravity, field theory and signatures of noncommutative spacetime

Szabo

2009

Gen Relativ Gravit

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A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.

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Section: Gravity In Noncommutative Gauge Theoriesmentioning

confidence: 98%

Quantum gravity, field theory and signatures of noncommutative spacetime

Szabo

2009

Gen Relativ Gravit

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“…The Seiberg-Witten map has also been instrumental in the formulation of noncommutative gravity theories: see, for instance, Refs. [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Seiberg-Witten map, itsθ-exact expansion, and the antifield formalism

Martı́n

Navarro

2015

Phys. Rev. D

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We deduce an evolution equation for an arbitrary hybrid Seiberg-Witten map for compact gauge groups by using the antifield formalism. We show how this evolution equation can be used to obtain the hybrid Seiberg-Witten map as an expansion, which is θ-exact, in the number of ordinary fields. We compute explicitly this expansion up to order three in the number of ordinary gauge fields and then particularize it to case of the Higgs of the noncommutative standard model.

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“…We find it encouraging that the self-dual option can be pursued to the extent shown in our paper, without any use of the Seiberg-Witten map or yet other techniques applied in the previous literature [24][25][26][27][28][29][30][31][32][33][34][35][36][37] Appendix A: Twist differential geometry…”

Section: Results and Open Problemsmentioning

confidence: 99%

Self-dual road to noncommutative gravity with twist: A new analysis

2014

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The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form should vanish, and that the Lorentz-Lie-algebravalued part of the full connection 1-form should be self-dual. Other two conditions, expressing self-duality of a pair 2-forms occurring in the full curvature 2-form, are also imposed. This leads to a systematic solution strategy, here displayed for the first time, where all parts of the connection 1-form are first evaluated, hence the full curvature 2-form, and eventually all parts of the tetrad 1-form, when expanded on the basis of γ-matrices. By assuming asymptotic expansions which hold up to first order in the noncommutativity matrix in the neighbourhood of the vanishing value for noncommutativity, we find a family of self-dual solutions of the field equations. This is generated by solving first a inhomogeneous wave equation on 1-forms in a classical curved spacetime (which is itself self-dual and solves the vacuum Einstein equations), subject to the Lorenz gauge condition.In particular, when the classical undeformed geometry is Kasner spacetime, the above scheme is fully computable out of solutions of the scalar wave equation in such a Kasner model.

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Seiberg-Witten maps forSO(1,3)gauge invariance and deformations of gravity

Cited by 16 publications

References 36 publications

Quantum gravity, field theory and signatures of noncommutative spacetime

Quantum gravity, field theory and signatures of noncommutative spacetime

Hybrid Seiberg-Witten map, itsθ-exact expansion, and the antifield formalism

Self-dual road to noncommutative gravity with twist: A new analysis

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