Two Dimensional Gauge Theoretic Supergravities

TL;DR

This paper explores two-dimensional supergravity models, demonstrating their topological gauge invariance, and introduces new models based on graded algebra extensions that satisfy specific curvature conditions.

Contribution

It proves the topological gauge invariance of a supersymmetric extension of the Jackiw-Teiltelboim model and proposes new supergravity models based on graded algebra extensions.

Findings

The supersymmetric Jackiw-Teiltelboim extension is topological and gauge invariant.

The string-inspired dilaton gravity model does not fit into a topological gauge framework.

New models based on graded Poincaré algebra satisfy a vanishing curvature condition.

Abstract

We investigate two dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. We concentrate on four models. The first model is the $N=1$ supersymmetric extension of Jackiw-Teiltelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki, and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equation of motions correspond to the supergravity ones and gauge transformations encompass local supersymmetries, but also we identify the $\int \langle \eta, F\rangle$-theory with the superfield formalism action written by Chamseddine. Next, we show that the $N=1$ supersymmetric extension of string inspired two dimensional dilaton gravity put forward by Park and Strominger is a theory that satisfies a non-vanishing curvature condition and cannot be written as a $\int\langle \eta,F\rangle$-theory. As an alternative, we propose two examples of topological and gauge invariant theories that are based on graded extension of the extended Poincar\'e algebra and satisfy a vanishing curvature condition. Both models are interpreted as supersymmetric extensions of the string inspired dilaton gravity.