Four-dimensional topological Einstein-Maxwell gravity

TL;DR

This paper formulates a topological version of four-dimensional Einstein-Maxwell gravity, deriving it from supergravity, and explores its symmetries, BRST invariance, and topological operators, providing a new perspective on the theory's structure.

Contribution

It explicitly constructs the complete on-shell action of topological Einstein-Maxwell gravity and relates it to Euclidean N=2 supergravity, detailing its symmetries and topological operators.

Findings

BRST-exact action and stress tensor

BRST-invariant topological operators

Supersymmetry algebra with twisted symmetries

Abstract

The complete on-shell action of topological Einstein-Maxwell gravity in four-dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N=2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.