Seven--Superform Gauge Fields in N=1, D=10 Supergravity and Duality

TL;DR

This paper develops a superspace formulation of 10-dimensional N=1 supergravity that incorporates dual gauge fields of various forms, linking them through duality and aiming to connect to string theory compactifications.

Contribution

It introduces a novel superspace framework for supergravity with dual 2- and 6-forms, extending the gauge field content and relating to string theory dualities.

Findings

Duality interchanges Bianchi identities and equations of motion.

Reformulation involves 7-forms as gauge fields in supergravity.

Connections to SL(2,R) symmetry in string compactifications.

Abstract

We present a formulation of $N=1,D=10$ Supergravity--Super--Maxwell theory in superspace in which the graviphoton can be described by a 2--form $B_2$ or a 6--form $B_6$, the photon by a 1--form $A_1$ or a 7--form $A_7$ and the dilaton by a scalar $\varphi$ or an 8--form $\varphi_8$, the supercurvatures of these fields being related by duality. Duality interchanges Bianchi identities and equations of motion for each of the three couples of fields. This construction envisages the reformulation of $D=10$ Supergravity, involving 7--forms as gauge fields, conjectured by Schwarz and Sen, which, upon toroidal compactification to four dimensions, gives the manifestly $SL(2,R)_S$ invariant form of the heterotic string effective action.