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- Title
THE SEIBERG-WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY.
- Authors
DI GREZIA, ELISABETTA; ESPOSITO, GIAMPIERO; FIGLIOLIA, MARCO; VITALE, PATRIZIA
- Abstract
In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg-Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg-Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.
- Subjects
SEIBERG-Witten invariants; YANG-Mills theory; GRAVITY; NONCOMMUTATIVE differential geometry; MATHEMATICAL mappings; NUMERICAL solutions to Einstein field equations; GENERAL relativity (Physics); ELECTRODYNAMICS
- Publication
International Journal of Geometric Methods in Modern Physics, 2013, Vol 10, Issue 6, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887813500230