How to halve maximal supergravity

197

397

We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but not necessary. We then analyze compactifications of DFT on twisted double tori satisfying the consistency conditions. The effective theory is a Gauged DFT where the gaugings come from the duality twists. The action, bracket, global symmetries, gauge symmetries and their closure are computed by twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic string and lower dimensional gauged supergravities are particular examples of Gauged DFT.

Section: Completing the Actionsupporting

confidence: 55%

Gauged double field theory

Graña

Marqués

2012

197

397

“…As was mentioned in section 1, the constraints of the GDFT (of the NS-NS sector) are in one-to-one correspondence with the constraints of half-maximal gauged supergravities. This extra condition we have found implies that the gauged theory in hand corresponds to a truncation of maximal supergavity [54,55]. We also note that the gauge invariance of the duality relations (4.42) can also be verified easily, and does not impose any extra constraints.…”

Section: Jhep09(2017)044supporting

confidence: 53%

“…In addition, we have shown here that the requirement of gauge invariance in the RR sector imposes the extra constraint (4.67), which also appeared in [23]. It is known that any half-maximal gauged supergravity that satisfies this constraint can be uplifted to maximal gauged supergavity [54,55]. Therefore, the existence of this extra constraint can be seen as a sign that the reduction we have studied here should be related to duality twisted reductions of Exceptional Field Theory (EFT), which is a U-duality invariant extension of supergravity [56][57][58][59].…”

Section: Jhep09(2017)044mentioning

confidence: 63%

Duality twisted reductions of Double Field Theory of Type II strings

Özer

2017

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.

“…The different components of the projector onto the 133 representation read [59,60] P (adj)îmnk plq = − 1 2 ǫî ǫkl δ pq mn + 1 12…”

Section: Jhep06(2013)046mentioning

confidence: 99%

Extended geometry and gauged maximal supergravity

Aldazábal

Graña

Marqués

et al. 2013

119

185

We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E 7(7) . Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.