Abstract
We obtain massive deformations of Type IIA supergravity theory through duality twisted reductions of Double Field Theory (DFT) of massless Type II strings. The mass deformation is induced through the reduction of the DFT of the RR sector. Such reductions are determined by a twist element belonging to Spin+(10, 10), which is the duality group of the DFT of the RR sector. We determine the form of the twists and give particular examples of twists matrices, for which a massive deformation of Type IIA theory can be obtained. In one of the cases, requirement of gauge invariance of the RR sector implies that the dilaton field must pick up a linear dependence on one of the dual coordinates. In another case, the choice of the twist matrix violates the weak and the strong constraints explicitly in the internal doubled space.
Highlights
That in the supergravity frame this new action reduces to the democratic formulation of the RR sector of Type II supergravity
Such reductions are determined by a twist element belonging to Spin+(10, 10), which is the duality group of the Double Field Theory (DFT) of the RR sector
In one of the cases, requirement of gauge invariance of the RR sector implies that the dilaton field must pick up a linear dependence on one of the dual coordinates
Summary
We give a very brief review of DFT and its duality twisted reduction. The DFT action would be invariant under the above transformations with a general Pin(d, d) element S, the chirality of the spinor field χ is preserved only by the Spin(d, d) subgroup. The requirement of consistency of the reduction of the DFT of the RR sector brings in one more condition: the fluxes should satisfy fABC f ABC = 0 Without this extra condition the reduced action cannot be invariant under the reduced gauge transformation rules. We have defined ξM (X, Y ) = (U −1)MAξA(X), λ(X, Y ) = e−ρ(Y )S(Y )λ(X), δξχ = S(Y ) δξχ), and δξλ = S(Y ) δλχ) It was shown in [34] that the reduced Lagrangian (2.30) is invariant under the deformed gauge transformations with parameter λ, only when the Dirac operator ∇/ is nilpotent. We would like to note that in finding the reduced Lagrangian and the gauge transformations, the following identity, which follows from the fact that the Lie algebras of SO(d, d) and Spin(d, d) are isomorphic plays a crucial role [34]: ΓA (U −1)MAS−1∂M
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