Scaling Symmetry and Carrollian Gravity

Abstract

We formulate matter-coupled scaling-Carroll gravity as a gauge theory and develop a conformal construction for generating local Carroll-invariant couplings. The construction relaxes Carrollian special conformal symmetry and leads to an enlarged gravity multiplet. After fixing the scaling symmetry, the theory is governed by the trace of the extrinsic curvature, the Carroll boost symmetry, a vector field descending from dilatation, and a symmetric tensor originating from the Carroll boost connection. The vector field acquires a Stückelberg-like transformation under Carroll boosts proportional to the trace of the extrinsic curvature. We show that appropriate gauge choices and field redefinitions give rise to Carrollian and Aristotelian descriptions, as well as a tensor-gauge description of the symmetric tensor field coupled to Aristotelian geometry. In the latter description, the Carroll boost parameter plays the role of a vector-valued gauge parameter.

31 pages, v2: fixing typos, clarification and ref. added, few errors corrected, main results unchanged, v3: section 4 revised (interpretations clarified), abstract and conclusion improved, ref. added, to be published in JHEP

References in corpus (27)

• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Carrollian Physics at the Black Hole Horizon
• Flat holography and Carrollian fluids
• Conformal Carroll groups
• Carroll versus Galilei Gravity
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Fractons, dipole symmetries and curved spacetime
• Carroll Expansion of General Relativity
• Magnetic Carrollian gravity from the Carroll algebra
• Carroll/fracton particles and their correspondence
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Carroll black holes
• Carrollian fluids and spontaneous breaking of boost symmetry
• The Symmetries of the Carroll Superparticle
• Non-Lorentzian theories with and without constraints
• Carrollian Origin of Spacetime Subsystem Symmetry
• Scale Invariance in Newton-Cartan and Hořava-Lifshitz Gravity
• Foundations of Carrollian Geometry
• Classification of Conformal Carroll Algebras
• Covariant Poisson's equation in torsional Newton-Cartan gravity
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Anisotropic conformal Carroll field theories and their gravity duals