Scaling Symmetry and Carrollian Gravity

TL;DR

This paper develops a gauge-theoretic formulation of matter-coupled scaling-Carroll gravity, revealing its connections to various regimes including Carroll, Aristotelian, and fracton gauge theories, and highlighting the role of symmetries and geometric constraints.

Contribution

It introduces a novel gauge theory framework for scaling-Carroll gravity and explores its different regimes and symmetry structures.

Findings

Identification of regimes including Carroll and Aristotelian gravity

Connection between fracton gauge theory and Carroll boost symmetry

Gauge choices lead to distinct geometric and dynamical phases

Abstract

We formulate matter-coupled scaling-Carroll gravity as a gauge theory and analyze its associated gravity multiplet. After fixing the scaling symmetry, the theory is governed by the trace of the extrinsic curvature, the Carroll boost symmetry, and a vector field descending from dilatation. We show that appropriate gauge choices and geometric constraints lead to distinct regimes, including dynamical Carroll gravity, Aristotelian gravity, and a fracton gauge theory coupled to Aristotelian geometry. In the fracton phase, the Carroll boost parameter plays the role of a vector-charge gauge symmetry.