Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions

TL;DR

This paper uncovers a new symmetry in two-dimensional non-Einsteinian gravity models, revealing an algebraic structure that explains their integrability and conserved quantities.

Contribution

It introduces a quadratically deformed $iso(2,1)$-algebra symmetry underlying $R^2$-gravity with torsion in two dimensions, providing new insights into its integrability.

Findings

Identifies an ultralocal symmetry in the Hamiltonian formulation.

Shows the algebraic structure as a deformation of $iso(2,1)$.

Connects algebra contractions to solution limits.

Abstract

The integrability of $R^2$-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed $iso(2,1)$-algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the centre of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.