https://doi.org/10.1140/epjs/s11734-023-00833-5
Review
Noncommutative 
gauge theory of gravity
Faculty of Physics, University of Belgrade, Studentski Trg 12-16, 11000, Belgrade, Serbia
Received:
31
July
2022
Accepted:
28
March
2023
Published online:
5
May
2023
Topological gravity (in the sense that it is metric-independent) in a 2n-dimensional spacetime can be formulated as a gauge field theory for the AdS gauge group 
by adding a multiplet of scalar fields. These scalars can break the gauge invariance of the topological gravity action, thus making a connection with Einstein’s gravity. This review is about a noncommutative (NC) star-product deformation of the four-dimensional AdS gauge theory of gravity, including Dirac spinors and the Yang–Mills field. In general, NC actions can be expanded in powers of the canonical noncommutativity parameter 
using the Seiberg–Witten map. The leading-order term of the expansion is the classical action, while the higher-order -dependent terms are interpreted as new types of coupling between classical fields due to spacetime noncommutativity. We study how these perturbative NC corrections affect the field equations of motion and derive some phenomenological consequences, such as NC-deformed Landau levels of an electron. Finally, we discuss how topological gravity in four dimensions (both classical and noncommutative) appears as a low-energy sector of five-dimensional Chern–Simons gauge theory in the sense of Kaluza–Klein reduction.
Noncommutativity and Physics. Guest editors: George Zoupanos, Konstantinos Anagnostopoulos, Peter Schupp.
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