Odd Scalar Curvature in Field-Antifield Formalism

Understand

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian.

• Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable.
• It turns out that the odd function \nu is not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density \rho.
• The main impact of introducing the \nu term is that it makes compatibility relations between E and \rho obsolete.