Topological Gravity on $(D,N)-$Shift Superspace Formulation

TL;DR

This paper revisits topological gravity using Shift Supersymmetry formalism, extending the action to arbitrary dimensions via BF-type gauge-fixing within a BV framework, providing a novel superspace approach.

Contribution

It introduces a new formulation of topological gravity in arbitrary dimensions using Shift Superspace and BF-type gauge-fixing methods.

Findings

Extended topological gravity action to arbitrary dimensions.

Applied BV formalism with ghost and anti-ghost superfields.

Provided a superspace formulation for topological gravity.

Abstract

In this contribution, we re-assess the subject of topological gravity by following the Shift Supersymmetry formalism. The gauge-fixing of the theory goes under the Batallin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and anti-ghost superfields, associated to the super-vielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on the gauge-fixing for BF-type models.