Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals

TL;DR

This paper extends the character expansion method to supergroups, enabling the calculation of new supergroup integrals such as the superversion of the Leutwyler-Smilga and Berezin-Karpelevich integrals, which were previously uncalculated.

Contribution

The paper introduces a novel extension of the character expansion method to supergroups, allowing for the calculation of previously unknown supergroup integrals.

Findings

Calculated a superversion of the Leutwyler-Smilga integral for the first time.

Generalized a superversion of the Berezin-Karpelevich integral.

Proposed a method applicable to other supergroup integrals.

Abstract

We introduce an extension of the character expansion method to the case of supergroups. This method allows us to calculate a superversion of the Leutwyler-Smilga integral which, to the best of our knowledge, has not been calculated before. We also use the method to generalize a previously calculated superversion of the Berezin-Karpelevich integral. Our character expansion method should also allow for the calculation of other supergroup integrals.