Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories

Abstract

In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS Carroll type. We also present the construction of the gravity theories based on the aforementioned algebras. In particular, the expansion method based on semigroups also allows to derive the (non-degenerate) invariant bilinear forms, ensuring the proper construction of the Chern-Simons gravity actions. Interestingly, in the vanishing cosmological constant limit we recover the spin-3 extensions of the infinite-dimensional Galilean and infinite-dimensional Carroll gravity theories.

Review on non-relativistic gravity

“…A generalization of NRG for arbitrary codimension foliation was presented in [118]. Two further generalizations include a non-relativistic version of spin-3 CS gravity [119,120] and multi-metric gravity [121].…”

Quantum Carroll/fracton particles

“…Even though most of the discussion has concentrated on free theories, it is worth exploring the potential application of our analysis to interacting theories. Some carrollian/fractonic models with non-trivial interactions include selfinteracting fracton scalar field theories and their coupling to fracton electrodynamics [28,35,37,38], Carroll scalar fields and their coupling to Carroll electrodynamics [22,[39][40][41], theories of Yang-Mills type [42,43], Carrollian gravity [21,[44][45][46][47][48][49][50][51][52][53][54], lower dimensional Chern-Simons theories [55][56][57] or extensions thereof [58][59][60], Carrollian JT or dilaton gravity [61,62] or their supergravity versions [63], and theories with spacetime subsystem symmetries [64,65]. An extensive list of references can be found in the reviews [5,6,66].…”

Non-Lorentzian theories with and without constraints

“…Some of the models we construct in this way are new to the best of our knowledge and we give some preliminary analysis of their physical significance. It would be very interesting to extend our analysis to gravity, possibly producing new non-Lorentzian gravitational models beyond the ones already known [8,10,14,25,27,36,37].…”