Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension
1
Physics Department, Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
2
Department of Physics, Berry College, Mount Berry, GA 30149, USA
3
IU Center for Spacetime Symmetries, Indiana University, Bloomington, IN 47405, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 480; https://doi.org/10.3390/sym10100480
Received: 3 September 2018 / Revised: 1 October 2018 / Accepted: 3 October 2018 / Published: 11 October 2018
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.
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Keywords:
Lorentz violation; noncommutative geometry; gravity
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MDPI and ACS Style
Bailey, Q.G.; Lane, C.D. Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension. Symmetry 2018, 10, 480. https://doi.org/10.3390/sym10100480
AMA Style
Bailey QG, Lane CD. Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension. Symmetry. 2018; 10(10):480. https://doi.org/10.3390/sym10100480
Chicago/Turabian StyleBailey, Quentin G., and Charles D. Lane 2018. "Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension" Symmetry 10, no. 10: 480. https://doi.org/10.3390/sym10100480
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