Extended geometry and gauged maximal supergravity

Aldazábal, G.; Graña, Mariana; Marqués, Diego; Rosabal, J. A.

doi:10.1007/jhep06(2013)046

Cited by 119 publications

(192 citation statements)

References 88 publications

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“…Our starting point will be the generalised E 7 × R + transformation [25,38] which in a given local generalised patch reads…”

Section: Summary Of Previous Resultsmentioning

confidence: 99%

“…The extended field theory, as the counterpart of double field theory, was first presented in [22,23], for d = 4, 5 and for d = 6, 7 using the E 11 non linear formalism in [24]. The geometric counterpart of DFT for the E 7 group in d = 7 was developed in [25]. In this work the relation between the four dimensional gauged maximal supergravity theory [26] and the U-duality extended E d × R + theory was pointed out.…”

Section: Jhep09(2015)153mentioning

confidence: 99%

“…There are at least two known solutions of the section condition [25]. Here, we are interested in making contact with the generalised geometry approach [20], for this reason we only focus on the SL(8) decomposition of (2.1).…”

Section: Jhep09(2015)153mentioning

confidence: 99%

“…To compute the Leibniz property for (2.38) we introduce the ∆ operator which provides an elegant way to check the properties of covariance of the generalised objects. It is defined as [25,34,47]…”

Section: Consistency Conditionsmentioning

confidence: 99%

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On the exceptional generalised Lie derivative for d ≥ 7

Rosabal

2015

J. High Energ. Phys.

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In this work we revisit the E 8 × R + generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E 7 × R + one. Compared to its E d × R + , d ≤ 7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E 8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E 8 × R + generalised transformation on the construction of the d = 8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.

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“…Our starting point will be the generalised E 7 × R + transformation [25,38] which in a given local generalised patch reads…”

Section: Summary Of Previous Resultsmentioning

confidence: 99%

Section: Jhep09(2015)153mentioning

confidence: 99%

Section: Jhep09(2015)153mentioning

confidence: 99%

Section: Consistency Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

On the exceptional generalised Lie derivative for d ≥ 7

Rosabal

2015

J. High Energ. Phys.

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“…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]. Indeed, the reduction of EFT on generalised parallelisable manifolds [60] (which corresponds to a reduction with a duality twisted anzats of the type we have considered here) gives rise to maximal gauged supergravity upon imposing a section constraint, which is the analogue of the strong constraint of DFT [61][62][63]. A flux formulation of (a particular type of) EFT is also available and geometric and non-geometric RR fluxes were studied also in this formulation [64].…”

Section: Jhep09(2017)044mentioning

confidence: 94%

Duality twisted reductions of Double Field Theory of Type II strings

Özer

2017

J. High Energ. Phys.

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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.

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The intriguing structure of non‐geometric frames in string theory

Blumenhagen

Deser

Plauschinn

et al. 2013

Fortschritte der Physik

103

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Non-geometric frames in string theory are related to the geometric ones by certain local O(D, D) transformations, the so-called β-transforms. For each such transformation, we show that there exists both a natural field redefinition of the metric and the Kalb-Ramond two-form as well as an associated Lie algebroid. We furthermore prove that the all-order low-energy effective action of the superstring, written in terms of the redefined fields, can be expressed through differential-geometric objects of the corresponding Lie algebroid. Thus, the latter provides a natural framework for effective superstring actions in non-geometric frames. Relations of this new formalism to double field theory and to the description of non-geometric backgrounds such as T-folds are discussed as well.R. Blumenhagen et al.: Non-geometric frames in string theory developed where the O(D, D) transformations 1 play a crucial role, namely generalized geometry [3][4][5][6] and double field theory (DFT) [7][8][9][10][11]. In the first approach, the concept of Riemannian geometry is extended from the tangent bundle T M to the generalized tangent bundle T M ⊕ T * M , whereas in the second the dimension of the space is doubled by including winding coordinates subject to certain constraints. For the latter construction, this admits a manifest global O(D, D) invariance of the action, so in particular, the action is manifestly invariant under T-duality transformations. The fundamental object in both approaches is a generalized metric which combines the usual metric and Kalb-Ramond field. The two local symmetries, diffeomorphisms and B-field gauge transformations, sit inside a subgroup of O (D, D). Their complement in O(D, D) contains so-called (local) β-transforms, which lead out of the usual geometric frame of string theory. Therefore, applying a local β-transform to the geometric frame leads to what we call a non-geometric frame.The existence of non-geometric backgrounds can be seen by analyzing the action of T-duality on the simple background of a flat three-dimensional torus with a constant H-flux [12]. Applying successive T-dualities, this H-flux is first mapped to a geometric flux [13] and by a second T-duality to the nongeometric Q-flux [14][15][16]. The latter background can be understood as a T-fold [17], where the transition functions between two charts involve T-duality transformations. A third T-duality is beyond the scope of the Buscher rules, and both non-commutative geometry [18][19][20] and conformal field theory [21-25] hint towards a non-associative structure. The effect of T-duality on brane solutions has been analyzed recently in [26].Since in DFT a global O(D, D) symmetry is manifest, the first-order effective action in at least a subset of these non-geometric frames is also described by it. What has been puzzling is that the DFT action cannot be straightforwardly interpreted as the Einstein-Hilbert action of some O(D, D) covariant differential geometry [27,28]. The problem is that the notions of torsion and curvature have to be c...

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Extended geometry and gauged maximal supergravity

Cited by 119 publications

References 88 publications

On the exceptional generalised Lie derivative for d ≥ 7

On the exceptional generalised Lie derivative for d ≥ 7

Duality twisted reductions of Double Field Theory of Type II strings

The intriguing structure of non‐geometric frames in string theory

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