Localization and Stationary Phase Approximation on Supermanifolds

Abstract

Given an odd vector field $Q$ on a supermanifold $M$ and a $Q$-invariant density $\mu$ on $M$, under certain compactness conditions on $Q$, the value of the integral ${\int }_M\mu$ is determined by the value of $\mu$ on any neighborhood of the vanishing locus $N$ of $Q$. We present a formula for the integral in the case where $N$ is a subsupermanifold which is appropriately non-degenerate with respect to $Q$. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend stationary phase approximation and the Morse-Bott Lemma to supermanifolds.

22 pages

References in corpus (1)

• Localization techniques in quantum field theories

Cited by in corpus (1)

• Equivariant localization in Batalin-Vilkovisky formalism