Ramond-Ramond cohomology and O(D, D) T-duality

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 Spin + (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 Spin + (10, 10) element S in the RR sector, then the NS-NS sector should also be deformed via the duality twist U = ρ(S), where ρ is the double covering homomorphism between P in(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.

Section: Jhep09(2017)044mentioning

confidence: 99%

Duality twisted reductions of Double Field Theory of Type II strings

Özer

2017

“…massive type II theories [11][12][13][14], and their supersymmetric extensions [1,[15][16][17][18], and also leads to a compelling generalization of Riemannian geometry [1,[19][20][21][22][23][24], which in turn is closely related to (and an extension of) results in the 'generalized geometry' of Hitchin and Gualtieri [25][26][27] (see [28][29][30][31][32][33][34] for other applications and [35][36][37][38] for reviews).…”

Section: Jhep09(2013)080mentioning

confidence: 99%

“…Putting everything together, the total variation of the improved Einstein-Hilbert term reads 14) up to total derivatives. Notice that the second term from (4.13) actually drops out in here by the antisymmetry of F .…”

Section: Jhep09(2013)080mentioning

confidence: 99%

U-duality covariant gravity

Hohm¹,

Samtleben

2013

107

Abstract:We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D = 11 supergravity. In this paper we work out a (3 + 3)-dimensional 'U-duality covariantization' of D = 4 Einstein gravity, in which the Ehlers group SL(2, R) is realized geometrically, acting in the 3 representation on half of the coordinates. We include the full (2 + 1)-dimensional metric, while the 'internal vielbein' is a coset representative of SL(2, R)/SO(2) and transforms under gauge transformations via generalized Lie derivatives. In addition, we introduce a gauge connection of the 'C-bracket', and a gauge connection of SL(2, R), albeit subject to constraints. The action takes the form of (2 + 1)-dimensional gravity coupled to a Chern-Simons-matter theory but encodes the complete D = 4 Einstein gravity. We comment on generalizations, such as an 'E 8(8) covariantization' of M-theory.

“…3 The methods have been successfully applied to construct Yang-Mills DFT [67], coupling to fermions [68], coupling to RR-sector [69], N = 1, D = 10 (full order) super DFT [70], N = 2, D = 10 (full order) super DFT [71], and the completely covariant string action on doubled-yet-gauged spacetime [61].…”

Section: Jhep06(2014)102mentioning

confidence: 99%

“…7 Compared to the ordinary Riemannian geometry, the existence of a projection operator and its key role appear to be novel distinct features of the extended-yet-gauged spacetime geometries, such as DFT-geometry in [65][66][67][68][69][70][71] and the present SL(N ) U-gravity.…”

Section: Projection Operatormentioning

confidence: 99%

U-gravity: SL(N)

Park

Suh

2014

Self Cite

We construct a duality manifest gravitational theory for the special linear group, SL(N ) with N = 4. The spacetime is formally extended, to have the dimension 1 2 N (N − 1), yet is gauged. Consequently the theory is subject to a section condition. We introduce a semi-covariant derivative and a semi-covariant 'Riemann' curvature, both of which can be completely covariantized after symmetrizing or contracting the SL(N ) vector indices properly. Fully covariant scalar and 'Ricci' curvatures then constitute the action and the 'Einstein' equation of motion. For N ≥ 5, the section condition admits duality inequivalent two solutions, one (N − 1)-dimensional and the other three-dimensional. In each case, the theory can describe not only Riemannian but also non-Riemannian backgrounds.