Self-Dual Forms in Supergeometry I: The Chiral Boson

TL;DR

This paper introduces a supergeometric approach using pseudoforms to construct models with self-dual fields, exemplified by the chiral boson in two dimensions, advancing the understanding of supergravity and quantum field theories.

Contribution

It develops a constructive method combining string field theory and supergeometry to model self-dual fields in superspaces for various backgrounds.

Findings

Established a new supergeometric framework for self-dual fields.

Applied the method explicitly to the chiral boson in two dimensions.

Opened new avenues in supergravity and quantum field theory research.

Abstract

Recent results of A. Sen on quantum field theory models with self-dual field strengths use string field theory as a starting point. In the present work, we show that combining string field theory and supergeometry we can provide a constructive method for all these models, for any superspace representation and for any given background. The analysis is based on the new concept of pseudoform, emerging in supergeometry, which opens a new page in quantum field theory and, in particular, in supergravity. The present work deals with an explicit example, the case of the chiral boson multiplet in d=2.