Supersymmetry and homogeneity of M-theory backgrounds

Figueroa-O’Farrill, José; Meessen, Patrick; Philip, Simon

doi:10.1088/0264-9381/22/1/014

Cited by 94 publications

(219 citation statements)

References 51 publications

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“…Hence these subgroups are already considered in [20], whence the novelty in this paper consists of extending the classification of N = 4 quotients by the inclusion of singular quotients. Since homogeneity implies smoothness, the fact that N > 4 orbifolds are actually smooth is of course consistent with the homogeneity conjecture [30][31][32] which says, in this context, that backgrounds preserving mode than half the supersymmetry are homogeneous.…”

Section: The Case Of Interestsupporting

confidence: 67%

Half-BPS M2-brane orbifolds

Medeiros

Figueroa-O’Farrill

2012

Advances in Theoretical and Mathematical Physics

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A. Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS 4 ×X 7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7-sphere by a freely-acting finite subgroup of SO(8). The classification is given in terms of ADE subgroups of the quaternions embedded in SO(8) as the graph of an automorphism. In this paper we extend this classification by dropping the requirement that the background be smooth, so that X is now allowed to be an orbifold of the round 7-sphere. We find that if the background preserves more than half of the supersymmetry, then it is automatically smooth in accordance with the homogeneity conjecture, but that there are many half-BPS orbifolds, most of them new. The classification is now given in terms of pairs of ADE subgroups of quaternions fibred over the same finite group. We classify such subgroups and then describe the resulting orbifolds in terms of iterated quotients. In most cases the resulting orbifold can be described as a sequence of cyclic quotients.

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Section: The Case Of Interestsupporting

confidence: 67%

Half-BPS M2-brane orbifolds

Medeiros

Figueroa-O’Farrill

2012

Advances in Theoretical and Mathematical Physics

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“…It is easy to show (see, for example, [6]) that this implies that k 0 consists of translations along the worldvolume of the brane. Similarly, the symmetry superalgebra of the M2-brane is the normaliser of the Killing superalgebra in the symmetry superalgebra of the Minkowski background, which is the Poincaré superalgebra.…”

Section: The Maximal Superalgebra Of the M2 Branementioning

confidence: 98%

On the maximal superalgebras of supersymmetric backgrounds

Figueroa-O’Farrill

Hackett-Jones

Moutsopoulos

et al. 2009

Class. Quantum Grav.

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Abstract. In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS 4 ×S 7 and find that is isomorphic to osp(1|32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS 4 ×S 7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement.

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“…in [16], and there is now a vast amount of literature on them. For more recent results on homogeneity see the work by Figueroa-O'Farrill et al in [14,12,13]. A systematic study of 4-dimensional pp-waves was undertaken by Jordan, Ehlers and Kundt in [17] (see the English republication [18] and also [10], where the name pp-wave for plane fronted with parallel rays was introduced).…”

Section: Background and Main Resultsmentioning

confidence: 99%

Locally homogeneous pp-waves

Globke

Leistner

2016

Journal of Geometry and Physics

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Abstract. We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on 2-forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classical result by Jordan, Ehlers and Kundt in dimension 4. Several examples show that our assumptions on indecomposability and the rank of the curvature are essential. Background and main resultsA semi-Riemannian manifold (M, g) is homogeneous if it admits a transitive action by a group of isometries. This means that for each pair of points p and q in M there is an isometry of (M, g) that maps p to q. In the spirit of Felix Klein's Erlanger Programm to characterise geometries by their symmetry group, homogeneous manifolds are fundamental building blocks in geometry. Homogeneity is strongly tied to the geometry and the curvature of a manifold. For example, homogeneous Riemannian manifolds are geodescially complete, and, as an example for the link to curvature, we recall the celebrated result that any Ricci-flat homogeneous Riemannian manifold is flat [3]. A weaker version of homogeneity which still guarantees that the manifold looks the same everywhere is local homogeneity: a semi-Riemannian manifold is locally homogeneous if for each pair of points p and q in M there is an isometry defined on a neighbourhood of p that maps p to q.Here we will study local homogeneity for a certain class of Lorentzian manifolds, the so-called pp-waves and the plane waves. Locally, an (n + 2)-dimensional pp-wave admits coordinates (x − , x 1 , . . . , x n , x + ) such that (1.1) g := 2dxwhere H = H(x 1 , . . . , x n , x + ) is a function not depending on x − . For a plane wave, this function is required to be quadratic in the x i 's with x + -dependent coefficients. In general, they are not homogeneous, but they admit a parallel null (i.e. non-zero and light-like) vector field. An invariant definition of pp-waves and plane waves is given as follows: A Lorentzian manifold (M, g) is a pp-wave if it admits a parallel null vector field V ∈ Γ(T M), i.e., V = 0, g(V, V ) = 0 and ∇V = 0, and if its curvature endomorphism R : Λ 2 T M → Λ 2 T M is non-zero and satisfies where V ⊥ := {X ∈ T M | g(X, V ) = 0}. A plane wave is a pp-wave with the additional conditionFour-dimensional pp-waves were discovered in a mathematical context by Brinkmann [7] as one class of Einstein spaces that can be mapped conformally onto each other. In physics, plane waves and pp-waves appeared in general relativity [11], where they continue to play an important role (see for example [6,17] for more references) as metrics for which the Einstein equations become linear and, when they solve these equations, describe the propagation of gravitational waves with flat surfaces as wave fronts. Later Penrose discovered that when "zooming in on null geodesics" every space-times has a plane wave as limit [22]. More recently, the conditions under which the hom...

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Supersymmetry and homogeneity of M-theory backgrounds

Cited by 94 publications

References 51 publications

Half-BPS M2-brane orbifolds

Half-BPS M2-brane orbifolds

On the maximal superalgebras of supersymmetric backgrounds

Locally homogeneous pp-waves

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