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An Invariant Action for Noncommutative Gravity in Four-Dimensions
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abstract
Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to $U(1,1)\times U(1,1).$ No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.
Forward citations
Cited by 2 Pith papers
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From the Unification of Conformal and Fuzzy Gravities with Internal Interactions to the $SO(10)$ GUT and the Particle Physics Standard Model
One-loop gauge coupling running gives intermediate scales from 10^10 to 10^13 GeV and GUT scales from 10^15 to 2x10^16 GeV for four SO(10) breaking chains of the conformal-gravity unification, with two high-scale scen...
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Noncommutative Gauge Theories and Gravity
The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.
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