Odd Scalar Curvature in Anti-Poisson Geometry

TL;DR

This paper establishes that the odd scalar curvature in anti-Poisson geometry is directly related to a zero-order term in the bla operator, extending previous results to degenerate manifolds with compatible two-forms.

Contribution

It proves that the odd scalar urvature corresponds to the zero-order term bla_{ ho} in anti-Poisson geometry, generalizing earlier findings to degenerate cases.

Findings

bla_{ ho} is the odd scalar curvature of a compatible torsion-free connection.

The result extends to degenerate anti-Poisson manifolds with a compatible two-form.

The odd scalar curvature influences two-loop order effects in field-antifield quantization.

Abstract

Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure \rho if a zero-order term \nu_{\rho} is added to the \Delta operator. The effects of this odd scalar term \nu_{\rho} become relevant at two-loop order. We prove that \nu_{\rho} is essentially the odd scalar curvature of an arbitrary torsion-free connection that is compatible with both the anti-Poisson structure E and the density \rho. This extends a previous result for non-degenerate antisymplectic manifolds to degenerate anti-Poisson manifolds that admit a compatible two-form.