Noncommutative Topological Half-flat Gravity

TL;DR

This paper develops a noncommutative framework for topological half-flat gravity in four dimensions, involving a deformed BRST symmetry and a noncommutative version of Plebanski's heavenly equation to characterize instanton moduli space.

Contribution

It introduces a novel noncommutative formulation of topological gravity with a deformed BRST symmetry and a new characterization of instanton moduli space.

Findings

Deformation of BRST symmetry in noncommutative topological gravity

Formulation of a noncommutative Plebanski's heavenly equation

Characterization of instanton moduli space in the noncommutative setting

Abstract

We formulate a noncommutative description of topological half-flat gravity in four dimensions. BRST symmetry of this topological gravity is deformed through a twisting of the usual BRST quantization of noncommutative gauge theories. Finally it is argued that resulting moduli space of instantons is characterized by the solutions of a noncommutative version of the Plebanski's heavenly equation.