Odd Scalar Curvature in Field-Antifield Formalism
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.arxiv.org/abs/0708.0400 |
| Doi | http://dx.doi.org/10.1063/1.2835485 |
| Field | Theoretical physics |
| Keywords | BV Field-Antifield Formalism; Odd Laplacian; Antisymplectic Geometry; Semidensity; Antisymplectic Connection; Odd Scalar Curvature. |
| Description | 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. We give a geometric interpretation of \nu as (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and Ricci-form-flat connection. Finally, we speculate on how the density \rho could be generalized to a non-flat line bundle connection. |
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