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G. Papadopoulos

Publications and source records attributed to G. Papadopoulos.

At least 73 records · Page 4Linked to original sources
arXiv2011

Static M-horizons

We determine the geometry of all static black hole horizons of M-theory preserving at least one supersymmetry. We demonstrate that all such horizons are either warped products R^{1,1} *_w S or AdS_2 *_w S, where S admits an appropriate Spin(7) or SU(4) structure respectively; and we derive the conditions imposed by supersymmetry on these structures. We show that for electric static horizons with Spin(7) structure, the near horizon geometry is a product R^{1,1} * S, where S is a compact Spin(7) holonomy manifold. For electric static solutions with SU(4) structure, we show that the horizon section S is a circle fibration over an 8-dimensional Kahler manifold which satisfies an additional condition involving the Ricci scalar and the length of the Ricci tensor. Solutions include AdS_2 * S^3 * CY_6 as well as many others constructed from taking the 8-dimensional Kahler manifold to be a product of Kahler-Einstein and Calabi-Yau spaces.

hep-th↗
arXiv2010

Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces

Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifold. We prove that the solutions depend on 6 functions which are determined by a non-linear differential system of 6 equations that include the Monge-Ampere equation. We show that this system has an explicit solution for the Kahler manifold S^2 X S^2. We also demonstrate that there is an associated cohomological system which has solutions on del Pezzo surfaces. We raise the question of whether for every solution of the cohomological problem there is a solution of the differential system, and so a new heterotic horizon. The horizon sections have topologies which include ((k-1) S^2 X S^4 # k (S^3 X S^3)) X T^2$ indicating the existence of exotic black holes. We also find an example of a horizon section which gives rise to two different near horizon geometries.

hep-th↗
arXiv2010

M-theory backgrounds with 30 Killing spinors are maximally supersymmetric

We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds.

hep-th↗
arXiv2010

Classification of IIB backgrounds with 28 supersymmetries

We show that all IIB backgrounds with strictly 28 supersymmetries are locally isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we demonstrate that all solutions with more than 26 supersymmetries and only 5-form flux are maximally supersymmetric. The N=28 plane wave solution is a superposition of the maximally supersymmetric IIB plane wave with a heterotic string solution. We investigate the propagation of strings in this background, find the spectrum and give the string light-cone Hamiltonian.

hep-th↗
arXiv2009

Invariant Killing spinors in 11D and type II supergravities

We present all isotropy groups and associated $Σ$ groups, up to discrete identifications of the component connected to the identity, of spinors of eleven-dimensional and type II supergravities. The $Σ$ groups are products of a Spin group and an R-symmetry group of a suitable lower dimensional supergravity theory. Using the case of SU(4)-invariant spinors as a paradigm, we demonstrate that the $Σ$ groups, and so the R-symmetry groups of lower-dimensional supergravity theories arising from compactifications, have disconnected components. These lead to discrete symmetry groups reminiscent of R-parity. We examine the role of disconnected components of the $Σ$ groups in the choice of Killing spinor representatives and in the context of compactifications.

hep-th↗
arXiv2009

Kundt Spacetimes

Kundt spacetimes are of great importance in general relativity in 4 dimensions and have a number of topical applications in higher dimensions in the context of string theory. The degenerate Kundt spacetimes have many special and unique mathematical properties, including their invariant curvature structure and their holonomy structure. We provide a rigorous geometrical kinematical definition of the general Kundt spacetime in 4 dimensions; essentially a Kundt spacetime is defined as one admitting a null vector that is geodesic, expansion-free, shear-free and twist-free. A Kundt spacetime is said to be degenerate if the preferred kinematic and curvature null frames are all aligned. The degenerate Kundt spacetimes are the only spacetimes in 4 dimensions that are not $\mathcal{I}$-non-degenerate, so that they are not determined by their scalar polynomial curvature invariants. We first discuss the non-aligned Kundt spacetimes, and then turn our attention to the degenerate Kundt spacetimes. The degenerate Kundt spacetimes are classified algebraically by the Riemann tensor and its covariant derivatives in the aligned kinematic frame; as an example, we classify Riemann type D degenerate Kundt spacetimes in which $\nabla(Riem),\nabla^{(2)}(Riem)$ are also of type D. We discuss other local characteristics of the degenerate Kundt spacetimes. Finally, we discuss degenerate Kundt spacetimes in higher dimensions.

gr-qc↗
arXiv2008

The Classification of Highly Supersymmetric Supergravity Solutions

The spinorial geometry method is an effective method for constructing systematic classifications of supersymmetric supergravity solutions. Recent work on analysing highly supersymmetric solutions in type IIB supergravity using this method is reviewed [arXiv:hep-th/0606049, arXiv:0710.1829]. It is shown that all supersymmetric solutions of IIB supergravity with more than 28 Killing spinors are locally maximally supersymmetric.

hep-th↗
arXiv2008

Geometry of all supersymmetric four-dimensional ${\cal N}=1$ supergravity backgrounds

We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four supercharges, coupled to any number of vector and scalar multiplets in all cases. We find that backgrounds with N=1 supersymmetry admit a null, integrable, Killing vector field. There are two classes of N=2 backgrounds. The spacetime in the first class admits a parallel null vector field and so it is a pp-wave. The spacetime of the other class admits three Killing vector fields, and a vector field that commutes with the three Killing directions. These backgrounds are of cohomogeneity one with homogenous sections either $\bR^{2,1}$ or $AdS_3$ and have an interpretation as domain walls. The N=3 backgrounds are locally maximally supersymmetric. There are N=3 backgrounds which arise as discrete identifications of maximally supersymmetric ones. The maximally supersymmetric backgrounds are locally isometric to either $\bR^{3,1}$ or $AdS_4$.

hep-th↗
arXiv2008

On the structure of k-Lie algebras

We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and confirms a conjecture in math/0211170.

hep-th↗
arXiv2008

M2-branes, 3-Lie Algebras and Plucker relations

We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a $\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.

hep-th↗
arXiv2008

Killing-Yano equations and G-structures

We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$. Solutions include nearly-Kähler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds. As an application, we find that particle probes on $AdS_4\times X$ compactifications of type IIA and 11-dimensional supergravity admit a ${\cal W}$-type of symmetry generated by the fundamental forms. We also explore the ${\cal W}$-symmetries of string and particle actions in heterotic and common sector supersymmetric backgrounds. In the heterotic case, the generators of the ${\cal W}$-symmetries completely characterize the solutions of the gravitino Killing spinor equation, and the structure constants of the ${\cal W}$-symmetry algebra depend on the solution of the dilatino Killing spinor equation.

hep-th↗
arXiv2008

IIB backgrounds with five-form flux

We investigate all N=2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups $Spin(7)\ltimes\bR^8$, $SU(4)\ltimes\bR^8$ and $G_2$. In the $SU(4)\ltimes\bR^8$ case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the $SU(4)\ltimes \bR^8$ structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The $G_2$ backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic $G_2$ structure. The $Spin(7)\ltimes\bR^8$ backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy $Spin(7)$. In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the $AdS_5$ black holes, lift to $SU(4)\ltimes\bR^8$ pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one $G_2$ manifold which has principal orbit $S^3\times S^3$.

hep-th↗
arXiv2007

IIB solutions with N>28 Killing spinors are maximally supersymmetric

We show that all IIB supergravity backgrounds which admit more than 28 Killing spinors are maximally supersymmetric. In particular, we find that for all N>28 backgrounds the supercovariant curvature vanishes, and that the quotients of maximally supersymmetric backgrounds either preserve all 32 or N<29 supersymmetries.

hep-th↗
arXiv2007

Geometry of all supersymmetric type I backgrounds

We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9,1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in the subgroup Sigma(P) of Spin(9,1) which preserves the space of parallel spinors P. Given a solution of the gravitino Killing spinor equation with L parallel spinors, L = 1,2,3,4,5,6,8, the dilatino Killing spinor equation allows for solutions with N supersymmetries for any 0 < N =< L. Moreover for L = 16, we confirm that N = 8,10,12,14,16. We find that in most cases the Bianchi identities and the field equations of type I backgrounds imply a further reduction of the holonomy of the supercovariant connection. In addition, we show that in some cases if the holonomy group of the supercovariant connection is precisely the isotropy group of the parallel spinors, then all parallel spinors are Killing and so there are no backgrounds with N < L supersymmetries.

hep-th↗
arXiv2006

Aspects of spinorial geometry

We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in terms of a linear system for the fluxes and the geometry of spacetime. The solutions of this linear system express some of the fluxes in terms of the spacetime geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. We also present some of the recent applications like the classification of maximally supersymmetric G-backgrounds in IIB, this includes the most general pp-wave solution preserving 1/2 supersymmetry, and the classification of N=31 backgrounds in ten and eleven dimensions.

hep-th↗
arXiv2006

Classification of supersymmetric backgrounds of string theory

We review the recent progress made towards the classification of supersymmetric solutions in ten and eleven dimensions with emphasis on those of IIB supergravity. In particular, the spinorial geometry method is outlined and adapted to nearly maximally supersymmetric backgrounds. We then demonstrate its effectiveness by classifying the maximally supersymmetric IIB G-backgrounds and by showing that N=31 IIB solutions do not exist.

hep-th↗
arXiv2006

N=31, D=11

We show that eleven-dimensional supergravity backgrounds with thirty one supersymmetries, N=31, admit an additional Killing spinor and so they are locally isometric to maximally supersymmetric ones. This rules out the existence of simply connected eleven-dimensional supergravity preons. We also show that N=15 solutions of type I supergravities are locally isometric to Minkowski spacetime.

hep-th↗