Incorporation of fermions into double field theory

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.

Five-brane actions in double field theory

“…The remaining bosonic fields of type II supergravity are the RR fields, and these form spinors of O(d, d), with the type II theories distinguished by chirality. Extensions of DFT to treat the RR fields and then supersymmetry were provided in [21][22][23][24][25][26]. A "split" or "Kaluza-Klein" formulation, in which not all directions are doubled, was provided for the NSNS sector in [27].…”

Gauged double field theory

“…The original formulation was done in [1][2][3][4], following previous ideas by Siegel [5,6] and Tseytlin [7,8] (see also [9,10]). Since then, DFT has been extended in many different ways [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]- [32]. Some very recent related works on duality based constructions are [33][34][35][36][37][38][39][40].…”

Higher Spin Representations of K(E10)

“…[8] the decomposition of e 10 under its so(9, 9) subalgebra was studied and shown to correspond to both type IIA and type IIB theory since the Ramond-Ramond potentials occurred in a spinor representation of so(9, 9) that can be read either as all even or all odd forms; similarly, the fermions arrange themselves correctly for the two theories [24]. In investigations of double field theory the same structure appears [25] and we have therefore dubbed this T-duality agnostic decomposition as 'doubled SUGRA. ' There are some additional subtleties associated with the global assignment of fermionic and bosonic representations at the group level.…”