Hamiltonian Approach to $2D$ Supergravity

TL;DR

This paper presents a covariant, gauge-independent Hamiltonian formulation of 2D supergravity derived from bosonic gravity, explicitly computing the superalgebra and proposing a method to incorporate nontrivial quantum effects.

Contribution

It introduces a novel covariant Hamiltonian approach to 2D supergravity, explicitly deriving the superalgebra and suggesting a new way to include quantum physics.

Findings

Superalgebra explicitly computed

Covariant, gauge-independent formulation developed

Potential for introducing nontrivial quantum effects

Abstract

We study $2D$ supergravity in a covariant and gauge independent way. The theory is obtained from $2D$ bosonic gravity following the square root method and the diffeomorphism superalgebra is explicitly computed. We argue that our approach could be a procedure for introducing nontrivial physics in quantum $2D$ (super)gravity.