Incorporation of fermions into double field theory

TL;DR

This paper extends double field theory to include fermions like gravitino and dilatino, maintaining covariance under T-duality and gauge symmetries, and explores the implications for type IIA and IIB supergravities.

Contribution

It introduces a covariant incorporation of fermions into double field theory, distinguishing between O(D,D) singlet and non-singlet fermions, and analyzes chirality flip under O(D,D) rotations.

Findings

Constructed covariant Dirac operators for fermions.

Identified criteria for O(D,D) rotations to flip fermion chirality.

Linked fermion sectors to type IIA and IIB supergravities.

Abstract

Based on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O(D,D) T-duality, diffeomorphism, one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We note that there are two kinds of fermions in double field theory: O(D,D) singlet and non-singlet which may be identified, respectively as the common and the non-common fermionic sectors in type IIA and IIB supergravities. For each kind, we construct corresponding covariant Dirac operators. Further, we derive a simple criterion for an O(D,D) rotation to flip the chirality of the O(D,D) non-singlet chiral fermions, which implies the exchange of type IIA and IIB supergravities.