A conformal approach to matter coupled Aristotelian gravity

TL;DR

This paper develops a conformal algebra framework for matter coupling in Aristotelian gravity, introducing new algebraic structures and constructing various gravity models lacking boost symmetries, relevant for fracton physics.

Contribution

It extends the Aristotelian algebra to conformal algebras with Minkowski and Euclidean signatures, enabling novel matter couplings and gravity models without boost invariance.

Findings

Constructed conformal extensions of Aristotelian algebra.

Developed electric and magnetic Aristotelian gravity models.

Explored matter couplings for quadratic and higher-derivative models.

Abstract

We show how to take the first step in the conformal program for constructing general matter couplings to Aristotelian gravity with arbitrary $p$-brane foliation. For this purpose we extend the $p$-brane Aristotelian algebra to the direct sum of two conformal algebras: one with Minkowski signature for the longitudinal directions and a second one with Euclidean signature for the transverse directions. For some cases, it is sufficient to work with a subalgebra of this conformal extension that, instead of two dilatations that are isotropic in either the longitudinal or transverse directions, contains a single dilatation that acts on the longitudinal and transverse directions in an an-isotropic way. Using this conformal extension we show how different electric and magnetic versions of Aristotelian gravity can be constructed that all have the distinguishing property that they are not invariant under any (Galilean or Carrollian) boost symmetry. We next consider several matter couplings both for quadratic-derivative models as well as for some higher-derivative models that have recently been considered in connection with studies on fractons.