Perturbative Quantum Gravity on Complex Spacetime

TL;DR

This paper explores non-anticommutative perturbative quantum gravity on complex spacetime, analyzing BRST symmetry, field shifts, and superspace formulations to advance understanding of quantum gravity in complex geometries.

Contribution

It introduces a BRST-invariant Lagrangian density for non-anticommutative quantum gravity on complex spacetime, utilizing the BV formalism and superspace methods.

Findings

BRST symmetry analysis of non-anticommutative quantum gravity

Construction of shift-invariant Lagrangian density in BV formalism

Superspace formulation of gauge-fixing and ghost terms

Abstract

In this paper we will study non-anticommutative perturbative quantum gravity on spacetime with a complex metric. After analysing the BRST symmetry of this non-anticommutative perturbative quantum gravity, we will also analyse the effect of shifting all the fields. We will construct a Lagrangian density which is invariant under the original BRST transformations and the shift transformations in the Batalin-Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this shift symmetry invariant Lagrangian density can be elegantly written down in superspace with a single Grassmann parameter.