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

J A Lourenço,W Spalenza,J A Helayël Neto

doi:10.1155/2018/2786081

Abstract

We reassess the subject of topological gravity by following the shift supersymmetry formalism. The gauge-fixing of the theory goes under the Batalin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and antighost superfields, associated with the supervielbein 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.

Highlights

Topological field theories have been introduced by Witten [1] and soon after applied in several areas that describe quantummechanical and quantum field-theoretical systems
A topological gravity theory may be formulated by gauge-fixing an action that is a topological invariant, which can be achieved by twisting an extended supergravity theory
We accomplished this construction by exploiting the shift supersymmetry formalism and defining the geometric supersymmetric elements

Summary

Introduction

Topological field theories have been introduced by Witten [1] and soon after applied in several areas that describe quantummechanical and quantum field-theoretical systems. We think it is possible to proceed seemingly for topological gravity [15], that is, to describe this theory by adopting a topological formulation based on supersymmetry (SUSY, on): a supersymmetric topological gravity [16] We accomplished this construction by exploiting the shift supersymmetry formalism and defining the geometric supersymmetric elements. We define these elements in a basis supermanifold M with a mapping to the Euclidian-flat-space carried out by D−bein This D−bein and the Lorentz connection describe the geometric sector along with the gauge-fixing fields of the theory in an Euclidean flat-space-time and the Grassmannvalued coordinates; the latter are adjoined to the space-time coordinates to constitute the superspace of the theory.

Generalized Gravity as a Super-BF Model

Concluding Comments