SL(2,C) gravity on noncommutative space with Poisson structure
High Energy Physics - Theory
2014-11-20 v4 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.
Cite
@article{arxiv.1004.2118,
title = {SL(2,C) gravity on noncommutative space with Poisson structure},
author = {Yan-Gang Miao and Shao-Jun Zhang},
journal= {arXiv preprint arXiv:1004.2118},
year = {2014}
}
Comments
12 pages, no figures; v2: 13 pages, clarifications and references added; v3: clarifications added; v4: more clarifications and references added, final version to appear in Phys. Rev. D