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Massive gravity: a primer. (English) Zbl 1263.83004

Calcagni, Gianluca (ed.) et al., Quantum gravity and quantum cosmology. Papers based on the presentations at the 6th Aegean school, Chora, Naxos Island, Greece, September 12–17, 2011. Berlin: Springer (ISBN 978-3-642-33035-3/pbk; 978-3-642-33036-0/ebook). Lecture Notes in Physics 863, 119-145 (2013).
Summary: We show that the recently constructed \(3D\) higher-derivative “new massive gravity theory” is the result of a general procedure that allows one to construct, in the free case, higher-derivative gauge theories for a wide class of “spins” in diverse dimensions. We specify the criterium that the “spin” and dimension need to satisfy in order for the construction to apply. To clarify the general procedure we present examples of higher-derivative gauge theories for the special cases of spin 1 in \(D=3,5\) and 7 dimensions. We next apply the procedure to spin 2 in \(D=3\) dimensions and show how the new massive gravity and topological massive gravity theories are constructed. Both theories allow interactions. We indicate how and under which conditions the \(3D\) new massive gravity theory can be extended to \(D=4\) dimensions and the \(3D\) topological massive gravity theory can be extended to \(D=7\) dimensions. We discuss the issue of interactions of these two theories.
For the entire collection see [Zbl 1254.83004].

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C80 Analogues of general relativity in lower dimensions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C45 Quantization of the gravitational field
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83E15 Kaluza-Klein and other higher-dimensional theories
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