Shape Dynamics in 2+1 Dimensions

Understand

Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance.

• In this paper we explicitly construct Shape Dynamics for a torus universe in 2+1 dimensions through a linking gauge theory that ensures dynamical equivalence with General Relativity.
• The Hamiltonian we obtain is formally a reduced phase space Hamiltonian.
• The construction of the Shape Dynamics Hamiltonian on higher genus surfaces is not explicitly possible, but we give an explicit expansion of the Shape Dynamics Hamiltonian for large CMC volume.