arXiv subjects

Klaus Behrndt

Publications and source records attributed to Klaus Behrndt.

At least 19 recordsLinked to original sources

arXiv2006

Classification of Supersymmetric Flux Vacua in M Theory

We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In particular, we find for N = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally Kähler for SU(2) structures, while for SU(3) structures the internal space has to be Einstein-Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure, where all fluxes are non-zero and the first order differential equations are solved.

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arXiv2006

Black Holes and Rings of minimal 5-dim. Supergravity

In this talk, I will summarize recent developments in 5-dimensional supergravity. Apart from black ring solutions, we will discuss the way of obtaining regular (bubbling) solutions with the same charges as black holes. We outline the procedure for the solution in five and four dimensions. Finally we explore the close relationship between 4- and 5-dimensional supersymmetric stationary solutions.

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arXiv2005

Exploring the relation between 4D and 5D BPS solutions

Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N=2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in Gödel-Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.

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arXiv2005

General Type IIB Fluxes with SU(3) Structures

A supersymmetric vacuum has to obey a set of constraints on fluxes as well as first order differential equations defined by the G-structures of the internal manifold. We solve these equations for type IIB supergravity with SU(3) structures. The 6-dimensional internal manifold has to be complex, the axion/dilaton is in general non-holomorphic and a cosmological constant is only possible if the SU(3) structures are broken to SU(2) structures. The general solution is expressed in terms of one function which is holomorphic in the three complex coordinates and if this holomorphic function is constant, we obtain a flow-type solution and near poles and zeros we find the so-called type-A and type-B vacuum.

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arXiv2005

Stabilization of moduli by fluxes

In order to lift the continuous moduli space of string vacua, non-trivial fluxes may be the essential input. In this talk I summarize aspects of two approaches to compactifications in the presence of fluxes: (i) generalized Scherk-Schwarz reductions and gauged supergravity and (ii) the description of flux-deformed geometries in terms of G-structures and intrinsic torsion.

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arXiv2004

General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory

We study conditions on general fluxes of massive Type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures imply that the internal space is constrained to be a nearly Kähler manifold with all the turned on fluxes, and the negative cosmological constant proportional to the mass parameter, and the dilaton fixed by the quantized ratio of the three-form and four-form fluxes. We further discuss the implications of such flux vacua with added intersecting D6-branes, leading to the chiral non-Abelian gauge sectors (without orientifold projections). Examples that break SU(3)-structures to SU(2)-ones allow for the internal space conformally flat (up to orbifold and orientifold projections), for which we give an explicit example. These results provide a starting point for further study of the four-dimensional (chiral) N = 1 supersymmetric solutions of massive Type IIA supergravity with D-branes and fluxes, compactified on orientifolds.

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arXiv2004

Black holes in Goedel-type universes with a cosmological constant

We discuss supersymmetric black holes embedded in a Goedel-type universe with cosmological constant in five dimensions. The spacetime is a fibration over a four-dimensional Kaehler base manifold, and generically has closed timelike curves. Asymptotically the space approaches a deformation of AdS_5, which suggests that the appearance of closed timelike curves should have an interpretation in some deformation of D=4, N=4 super-Yang-Mills theory. Finally, a Goedel-de Sitter universe is also presented and its causal structure is discussed.

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arXiv2004

Fluxes in M-theory on 7-manifolds: G_2-, SU(3)- and SU(2)-structures

We consider compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes, which leave at least four supercharges unbroken. Supersymmetric vacua admit G-structures and we discuss the cases of G_2-, SU(3)- as well as SU(2)-structures. We derive the constraints on the fluxes imposed by supersymmetry and determine the flux components that fix the resulting 4-dimensional cosmological constant (i.e. superpotential).

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arXiv2004

General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory

We derive conditions for the existence of four-dimensional \N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist only when the internal geometry is nearly-Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.

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arXiv2004

Fluxes in M-theory on 7-manifolds: G-structures and Superpotential

We consider compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes, which leave at least four supercharges unbroken. We focus especially on the case, where the 7-manifold supports two spinors which are SU(3) singlets and the fluxes appear as specific SU(3) structures. We derive the constraints on the fluxes imposed by supersymmetry and calculate the resulting 4-dimensional superpotential.

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arXiv2004

Superpotentials from flux compactifications of M-theory

In flux compactifications of M-theory a superpotential is generated whose explicit form depends on the structure group of the 7-dimensional internal manifold. In this note, we discuss superpotentials for the structure groups: G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For SU(3) structures, the non-zero flux components entering the superpotential describe an effective 1-dimensional model and a Chern-Simons model if there are SU(2) structures.

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arXiv2003

De Sitter vacua from N=2 gauged supergravity

Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories.

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arXiv2003

Chronological structure of a Goedel type universe with negative cosmological constant

We show that the Goedel solution of five-dimensional gauged supergravity contains either closed time-like curves through every space-time point or none at all, dependent on the rotational parameter. In addition, we present a deformation of that solution with a parameter kappa which characterizes the symmetry of four-dimensional base space: for kappa = 1, 0, -1 it has spherical, flat and hyperbolic symmetry, respectively. Also investigated are the causal properties of the lifted solution in 10 dimensions.

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arXiv2003

Supersymmetric Intersecting D6-branes and Fluxes in Massive Type IIA String Theory

We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS-NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold $X_6$ and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of $X_6$ that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2) and the D6-branes intersect at angles of SU(2) rotations; non-zero mass parameter corresponds to D8-branes which are orthogonal to the common cycle of all D6-branes. The anomaly inflow indicates that the gauge theory on intersecting (massive) D6-branes is not chiral.

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arXiv2003

Fluxes in M-theory on 7-manifolds and G structures

We consider warp compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes and investigate the constraints imposed by supersymmetry. As long as the 7-manifold supports only one Killing spinor we infer from the Killing spinor equations that non-trivial 4-form fluxes will necessarily curve the external 4-dimensional space. On the other hand, if the 7-manifold has at least two Killing spinors, there is a non-trivial Killing vector yielding a reduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxes can be incorporated if one includes non-trivial SU(3) structures.

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arXiv2003

Time-dependent backgrounds from supergravity with gauged non-compact R-symmetry

We obtain a general class of time-dependent, asymptotically de Sitter backgrounds which solve the first order bosonic equations that extremize the action for supergravity with gauged non-compact $R$-symmetry. These backgrounds correspond only to neutral fields with the correct sign of kinetic energy. Within N=2 five-dimensional supergravity with vector-superfields we provide examples of multi-centered charged black holes in asymptotic de Sitter space, whose spatial part is given by a time-dependent hyper-Kähler space. Reducing these backgrounds to four dimensions yields asymptotically de Sitter multi-centered charged black hole backgrounds and we show that they are related to an instanton configuration by a massive T-duality over time. Within N=2 gauged supergravity in four (and five)-dimensions with hyper-multiplets there could also be neutral cosmological backgrounds that are regular and correspond to the different de Sitter spaces at early and late times.

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arXiv2003

Intersecting branes from 7-manifolds with G_2 holonomy

In this talk I discuss intersecting brane configurations coming from explicit metrics with G_2 holonomy. An example of a 7-manifold which representing a R^3 bundle over a self-dual Einstein space is described and the potential appearing after compactification over the 6-d twistor space is derived.

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arXiv2002

Singular 7-manifolds with G_2 holonomy and intersecting 6-branes

A 7-manifold with G_2 holonomy can be constructed as a R^3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S^4 and CP^2 or its non-compact analogs. This 4-d Einstein space has four isometries and the fixed point set of a generic Killing vector is discussed. When embedded into M-theory the compactification over a given Killing vector gives intersecting 6-branes as IIA configuration and we argue that membrane instantons may resolve the curvature singularity.

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