Eur. Phys. J. C (2020) 80: 556
https://doi.org/10.1140/epjc/s10052-020-8090-8

Regular Article - Theoretical Physics

Spontaneously broken 3d Hietarinta/Maxwell Chern–Simons theory and minimal massive gravity

¹ School of Physics, Tomsk Polytechnic University, Lenin Ave. 30, 634050, Tomsk, Russia
² Department of Mathematics, Bogazici University, Bebek, 34342, Istanbul, Turkey
³ Max-Planck-Institut fur Gravitationsphysik (Albert-Einstein-Institut), Am Muhlenberg 1, D-14476, Potsdam, Germany
⁴ I.N.F.N., Sezione di Padova, Padua, Italy
⁵ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Via F. Marzolo 8, 35131, Padua, Italy

^* e-mail: dmitri.sorokin@pd.infn.it

Received: 3 March 2020
Accepted: 28 May 2020
Published online: 19 June 2020

Abstract

We show that minimal massive 3d gravity (MMG) of (Bergshoeff et al. in Class Quantum Grav 31:145008, 2014), as well as the topological massive gravity, are particular cases of a more general ‘minimal massive gravity’ theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern–Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.