Duality symmetry of the p-form effective action and super trace of the twisted de Rham complex

TL;DR

This paper investigates the duality symmetry of p-form fields coupled to a dilaton, linking the variation of their effective actions to the supertrace of the twisted de Rham complex across various manifold dimensions.

Contribution

It establishes a connection between the variation of effective actions under duality and the supertrace of the twisted de Rham complex, providing a general evaluation method for arbitrary manifolds.

Findings

Variation of effective actions is governed by the supertrace of the twisted de Rham complex.

Supertrace can be computed on manifolds of any dimension, with or without boundary.

The results deepen understanding of duality symmetry in quantum p-form fields.

Abstract

We consider quantum p-form fields interacting with a background dilaton. We calculate the variation with respect to the dilaton of a difference of the effective actions in the models related by a duality transformation. We show that this variation is defined essentially by the supertrace of the twisted de Rham complex. The supertrace is then evaluated on a manifold of an arbitrary dimension, with or without boundary.