Duality Twisted Reductions of Double Field Theory of Type II Strings

Abstract

We study duality twisted reductions of the Double Field Theory (DFT) of the RR sector of massless Type II theory, with twists belonging to the duality group $Spi{n}^{+}(10,10)$. We determine the action and the gauge algebra of the resulting theory and determine the conditions for consistency. In doing this, we work with the DFT action constructed by Hohm, Kwak and Zwiebach, which we rewrite in terms of the Mukai pairing: a natural bilinear form on the space of spinors, which is manifestly $Spin(n,n)$ invariant. If the duality twist is introduced via the $Spi{n}^{+}(10,10)$ element $S$ in the RR sector, then the NS-NS sector should also be deformed via the duality twist $U=\rho (S)$, where $\rho$ is the double covering homomorphism between $Pin(n,n)$ and $O(n,n)$. We show that the set of conditions required for the consistency of the reduction of the NS-NS sector are also crucial for the consistency of the reduction of the RR sector, owing to the fact that the Lie algebras of $Spin(n,n)$ and $SO(n,n)$ are isomorphic. In addition, requirement of gauge invariance imposes an extra constraint on the fluxes that determine the deformations.

chapter 4 revised and expanded, references added, published version

References in corpus (15)

• Double Field Theory
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Differential geometry with a projection: Application to double field theory
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Gauged N=4 supergravities
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Ramond-Ramond Cohomology and O(D,D) T-duality
• How to halve maximal supergravity
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions

Cited by in corpus (7)

• U-duality extension of Drinfel'd double
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-Abelian T-duality as a Transformation in Double Field Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality
• Yang-Mills sources in biconformal gravity