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The third way to 3D gravity

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Bergshoeff, E 
Merbis, W 
Routh, AJ 
Townsend, PK 


jats:p Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories. </jats:p>



Topologically massive gravity, bianchi identities, modified theories of gravity, lower-dimensional gravity

Journal Title

International Journal of Modern Physics D

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World Scientific Pub Co Pte Lt
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/L000636/1)
AJR is supported by a grant from the London Mathematical Society, and he would also like to thank the University of Groningen for hospitality during the writing of this essay.