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

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.