Generalized holonomy of M-theory vacua

Batrachenko, A.; Duff, M. J.; Liu, James T.; Wen, Weiling

doi:10.1016/j.nuclphysb.2005.07.029

Cited by 18 publications

(35 citation statements)

References 42 publications

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“…In a way, the field equations play the rôle of the torsion-free condition in the holonomy problem for affine connections. Except for the above result there are no other results of a general nature and although the infinitesimal holonomy of a number of solutions are known [31,32], a general pattern has yet to emerge.…”

Section: Supergravitymentioning

confidence: 87%

Lorentzian symmetric spaces in supergravity

Figueroa-O’Farrill

2008

ESI Lectures in Mathematics and Physics

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Abstract. I will discuss the emergence of lorentzian symmetric spaces as supersymmetric supergravity backgrounds. I will focus on supergravity theories in dimension 11, 10, and 6, and will concentrate on the determination of the so-called maximally supersymmetric backgrounds, for which a classification exists up to local isometry. A special class of lorentzian symmetric spaces also plays a rôle in the determination of parallelisable supergravity backgrounds in type II supergravity, which I will also summarise. (To appear in the proceedings of the programme Geometry of pseudo-riemannian manifolds with application to physics hosted by the Erwin Schrödinger International Institute for Mathematical Physics.)Mathematics Subject Classification (2000). Primary 53-B30; Secondary 83-50.

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Section: Supergravitymentioning

confidence: 87%

Lorentzian symmetric spaces in supergravity

Figueroa-O’Farrill

2008

ESI Lectures in Mathematics and Physics

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“…The generalized holonomy of these solutions, as well as several others, was originally investigated in [12]. For vacua with non-vanishing flux, including the brane solutions, it was seen that the Lie algebra generators obtained from first order integrability, (2.2), are insufficient for closure of the algebra.…”

Section: Generalized Holonomy Of the M5-branementioning

confidence: 99%

“…In particular, additional generators must be obtained by further commutators. In [12], this was done by closing the algebra by hand. In the present context, however, additional commutators are readily available from the higher order integrability expressions, (2.9).…”

Section: Generalized Holonomy Of the M5-branementioning

confidence: 99%

“…The first order integrability of the generalized connection, given by (2.2), was computed in [12]. The result was…”

Section: Generalized Holonomy Of the M5-branementioning

confidence: 99%

“…Other than this, however, the generalized holonomy groups SO(5) ⋉ 6R 4(4) for the M5-brane and SO(8) ⋉ 12R 2(8s) for the M2-brane identified in [12] are unchanged. Following this, we turn to the squashed S 7 [4,5], where the situation is considerably different.…”

Section: Introductionmentioning

confidence: 98%

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Higher order integrability in generalized holonomy

et al. 2007

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Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32, R), the Clifford group for eleven-dimensional spinors. Although previous investigations of generalized holonomy have focused on the curvature R M N (Ω) of the generalized SL(32, R) connection Ω M , we demonstrate that this local information is incomplete, and that satisfying the higher order integrability conditions is an essential feature of generalized holonomy. We also show that, while this result differs from the case of ordinary Riemannian holonomy, it is nevertheless compatible with the Ambrose-Singer holonomy theorem.

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Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra

Schulz

2004

Fortschritte der Physik

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Using a "Superstrings with Torsion" type description, we study a class of IIB orientifolds in which spacefilling O5 planes and D5 branes wrap the T 2 fiber in a warped modification of the product of 4D Minkowski space and a T 2 fibration. For the case that the base is T 4 , we provide examples that preserve 4D N = 1, 2, and 3 supersymmetry, both with internal RR flux, and with a combination of internal RR and NS flux. In these examples, the internal geometries admit integrable complex structure; however, the almost complex structure selected by the supersymmetry conditions is nonintegrable in the case that there is NS flux. We indicate explicitly the massless spectrum of gauge fields and moduli in each example. In a previous investigation, this class of orientifolds was studied using T-duality. Here, we extend the previous analysis, first by providing an intrinsic description that does not rely on duality, and then by elaborating on details of the T-duality map, which we use to check our results.

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Generalized holonomy of M-theory vacua

Cited by 18 publications

References 42 publications

Lorentzian symmetric spaces in supergravity

Lorentzian symmetric spaces in supergravity

Higher order integrability in generalized holonomy

Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra

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