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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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.
AMA Style
Bailey QG, Lane CD. Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension. Symmetry. 2018; 10(10):480.
Chicago/Turabian StyleBailey, Quentin G.; Lane, Charles D. 2018. "Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension" Symmetry 10, no. 10: 480.
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