Supersymmetric Configurations Research Articles

The general form of supersymmetric solutions of N = (1, 0) U(1) and SU(2) gauged supergravities in six dimensions

We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N = (1, 0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated with an structure. The structure is characterized by a null Killing vector which induces a natural 2 + 4 split of the six-dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four-dimensional Riemannian part, referred to as the base, obeys a second-order differential equation; surprisingly, for a large class of solutions the equation in the SU(2) theory requires the vanishing of the Weyl anomaly of N = 4 SYM on the base. Bosonic fluxes introduce torsion terms that deform the structure away from a covariantly constant one. The most general structure can be classified into terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is Kähler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left-hand spin bundle of the base. We employ our general ansatz to construct new solutions; we show that the U(1) theory admits a symmetric Cahen–Wallach4 × S2 solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is AdS3 × S3, which is supported by a self-dual 3-form flux and a meron on the S3. In the limit of the zero 3-form flux we obtain the Yang–Mills analogue of the Salam–Sezgin solution of the U(1) theory, namely R1,2 × S3. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.

A World-Volume Perspective on the Recombination of Intersecting Branes

We study brane recombination for supersymmetric configurations of intersecting branes in terms of the world-volume field theory. This field theory contains an impurity, corresponding to the degrees of freedom localized at the intersection. The Higgs branch, on which the impurity fields condense, consists of vacua for which the intersection is deformed into a smooth calibrated manifold. We show this explicitly using a superspace formalism for which the calibration equations arise naturally from F- and D-flatness.

Antiprotons in cosmic rays from neutralino annihilation

We calculate the antiproton flux due to relic neutralino annihilations, in a two-dimensional diffusion model compatible with stable and radioactive cosmic ray nuclei. We find that the uncertainty in the primary flux induced by the propagation parameters alone is about two orders of magnitude at low energies, and it is mainly determined by the lack of knowledge of the thickness of the diffusive halo. On the contrary, different dark matter density profiles do not significantly alter the flux: a Novarro-Frenk-White distribution produces fluxes which are at most 20% higher than an isothermal sphere. The most conservative choice for propagation parameters and dark matter distribution normalization, together with current data on cosmic antiprotons, cannot lead to any definitive constraint on the supersymmetric parameter space, either in a low-energy effective minimal supersymmetric standard model, or in a minimal supergravity scheme. However, if the best choice for propagation parameters---corresponding to a diffusive halo of $L=4\mathrm{kpc}$---is adopted, some supersymmetric configurations with the neutralino mass ${m}_{\ensuremath{\chi}}\ensuremath{\lesssim}100\mathrm{GeV}$ should be considered as excluded. An enhancement flux factor---due for instance to a clumpy dark halo or a higher local dark matter density---would imply a more severe cut on the supersymmetric parameters.

M5-brane geometries, T-duality and fluxes

We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture also provides a geometric interpretation for several properties of flux configurations (like the supersymmetry conditions, their contribution to tadpoles, etc), and for many non-trivial effects in the IIB side. Among the latter, the dielectric effect for probe D3-branes is dual to the recombination of probe M5-branes with background ones; also, a picture of a decay channel for non-supersymmetric fluxes is suggested.

The geometry ofD= 11 null Killing spinors

We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.

Supersymmetric solutions of minimal gauged supergravity in five dimensions

All purely bosonic supersymmetric solutions of minimal gauged supergravity in five dimensions are classified. The solutions fall into two classes depending on whether the Killing vector constructed from the Killing spinor is timelike or null. When it is timelike, the solutions are determined by a four-dimensional K\ahler base manifold, up to an antiholomorphic function, are necessarily not static, and generically preserve 1/2 of the supersymmetry. When it is null we provide a precise prescription for constructing the solutions and we show that they generically preserve 1/4 of the supersymmetry. We show that five-dimensional anti-de Sitter space $({\mathrm{AdS}}_{5})$ is the unique maximally supersymmetric configuration. The formalism is used to construct some new solutions, including a nonsingular deformation of ${\mathrm{AdS}}_{5},$ which can be uplifted to obtain new solutions of type IIB supergravity.

All supersymmetric solutions ofN= 2,D= 4 gauged supergravity

We classify all supersymmetric solutions of minimal gauged supergravity in four dimensions. There are two classes of solutions that are distinguished by the norm of the Killing vector constructed from the Killing spinor. If the Killing vector is timelike, the solutions are determined by the geometry of a two-dimensional base-manifold. When it is lightlike, the most general BPS solution is given by an electrovac AdS travelling wave. This supersymmetric configuration was previously unknown. Generically the solutions preserve one quarter of the supersymmetry. Also in the timelike case we show that there exist new BPS solutions, which are of Petrov type I, and are thus more general than the previously known type D configurations. These geometries can be uplifted to obtain new solutions of eleven-dimensional supergravity.

Supersymmetric dark matter in M31: can one see neutralino annihilation with CELESTE?

It is widely believed that dark matter exists within galaxies and clusters of galaxies. Under the assumption that this dark matter is composed of the lightest, stable supersymmetric particle, assumed to be the neutralino, the feasibility of its indirect detection via observations of a diffuse gamma-ray signal due to neutralino annihilations within M31 is examined. To this end, first the dark matter halo of the close spiral galaxy M31 is modelled from observations, then the resultant gamma-ray flux is estimated within supersymmetric model configurations. We conclude that under favourable conditions such as the rapid accretion of neutralinos on the central black hole in M31 and/or the presence of many clumps inside its halo with r −3/2 inner profiles, a neutralino annihilation gamma-ray signal is marginally detectable by the ongoing collaboration CELESTE.

The holonomy of the supercovariant connection and Killing spinors

We show that the holonomy of the supercovariant connection for M-theory backgrounds with $N$ Killing spinors reduces to a subgroup of $SL(32-N,\bR)\st (\oplus^N \bR^{32-N})$. We use this to give the necessary and sufficient conditions for a background to admit $N$ Killing spinors. We show that there is no topological obstruction for the existence of up to 22 Killing spinors in eleven-dimensional spacetime. We investigate the symmetry superalgebras of supersymmetric backgrounds and find that their structure constants are determined by an antisymmetric matrix. The Lie subalgebra of bosonic generators is related to a real form of a symplectic group. We show that there is a one-one correspondence between certain bases of the Cartan subalgebra of $sl(32, \bR)$ and supersymmetric planar probe M-brane configurations. A supersymmetric probe configuration can involve up to 31 linearly independent planar branes and preserves one supersymmetry. The space of supersymmetric planar probe M-brane configurations is preserved by an $SO(32,\bR)$ subgroup of $SL(32, \bR)$.

Supersymmetry and dark matter

There are only a handful of well-motivated WIMP-type particles that could act as the dark matter in the Universe. Supersymmetry provides a majority of them. The lightest neutralino remains the prime suspect. I present recent theoretical predictions for the neutralino direct detection. Today's experiments are already probing some allowed supersymmetric configurations but the experimental sensitivity has to improve by at least two orders of magnitude in order to reach the most plausible ranges of the spin-independent WIMP interaction cross section.

The geometry ofD= 11 Killing spinors

We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the former case we determine what kind of local SU(5) structure is present and show that almost all of the form of the geometry is determined by the structure. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D=11 Godel solution.

D-branes in PP-Waves and Massive Theories on Worldsheet with Boundary

We investigate the supersymmetric D-brane configurations in the pp-wave backgrounds proposed by Maldacena and Maoz. We study the surviving supersymmetry in a D-brane configuration from the worldvolume point of view. When we restrict ourselves to the background with N=(2,2) supersymmetry and no holomorphic Killing vector term, there are two types of supersymmetric D-branes: A-type and B-type. An A-type brane is wrapped on a special Lagrangian submanifold, and the imaginary part of the superpotential should be constant on its worldvolume. On the other hand, a B-type brane is wrapped on a complex submanifold, and the superpotential should be constant on its worldvolume. The results are almost consistent with the worldsheet theory in the lightcone gauge. The inclusion of gauge fields is also discussed and found BPS D-branes with the gauge field excitations. Furthermore, we consider the backgrounds with holomorphic Killing vector terms and N=(1,1) supersymmetric backgrounds.

Supersymmetric Boost on Intersecting D-branes

We study the effect of the Born-Infeld electric field on the supersymmetric configuration of various composite D-branes. We show that the generic values of the electric field do not affect the supersymmetry but, as it approaches $1/2\pi\alpha'$ keeping the magnetic field finite, various combinations of the magnetic fields allow up to 8 supersymmetries. We also explore the unbroken supersymmetries for two intersecting D-strings which are in uniform or relative motion. For a finite uniform Lorentz boost, 16 supersymmetries are guaranteed only when they are parallel. For an infinite one, 8 supersymmetries are preserved only when both the D-strings are oriented to the forward or backward direction of the boost. Under a finite relative boost, 8 supersymmetries are preserved only when the intersecting angle is less than $\pi/2$ and the intersecting point moves at the speed of light. As for an infinite relative boost, 8 supersymmetries are preserved regardless of the values of the intersecting angle.

Penrose limits of branes and marginal intersecting branes

We construct the Penrose limit backgrounds in closed forms along the generic null geodesics for the near-horizon geometries of D1, D3, D5, NS1 and NS5 branes. The Penrose limit metrics of D1, D5 and NS1 have non-trivial dependence of the light-cone time coordinate, while those of D3 and NS5 have no its dependence. We study the Penrose limits on the marginal 1/4 supersymmetric configurations of standard intersecting branes, such as the NS–NS intersection of NS1 and NS5, the RR intersections of Dp and Dq over some spatial dimensions and the mix intersections of NS5 and Dp over (p−1)-dimensional spaces. They are classified into three types that correspond to the Penrose limits of D1, D3 and D5 backgrounds.

Supersymmetric Intersecting Branes on the Type IIAT6/Bbb Z4Orientifold

We study supersymmetric intersecting D6-branes wrapping 3-cycles in the Type IIA T^6/Z_4 orientifold background. As a new feature, the 3-cycles in this orbifold space arise both from the untwisted and the Z_2 twisted sectors. We present an integral basis for the homology lattice, H_3(M,Z), in terms of fractional 3-cycles, for which the intersection form involves the Cartan matrix of E8. We show that these fractional D6-branes can be used to construct supersymmetric brane configurations realizing a three generation Pati-Salam model. Via brane recombination processes preserving supersymmetry, this GUT model can be broken down to a standard-like model.

FromD-bar D Pairs to Branes in Motion

We investigate various supersymmetric brane intersections. Motivated by the recent results on supertubes, we investigate general constraints in which parallel brane-antibrane configurations are supersymmetric. Dual descriptions of these configurations involve systems of branes in relative motion. In particular, we find new supersymmetric configurations which are not related to a static brane intersection by a boost. In these new configurations, the intersection point moves at the speed of light. These systems provide interesting time dependent backgrounds for open strings.

Local models for intersecting brane worlds

We describe the construction of configurations of D6-branes wrapped on compact 3-cycles intersecting at points in non-compact Calabi-Yau threefolds. Such constructions provide local models of intersecting brane worlds, and describe sectors of four-dimensional gauge theories with chiral fermions. We present several classes of non-compact manifolds with compact 3-cycles intersecting at points, and discuss the rules required for model building with wrapped D6-branes. The rules to build 3-cycles are simple, and allow easy computation of chiral spectra, RR tadpoles and the amount of preserved supersymmetry. We present several explicit examples of these constructions, some of which have Standard Model like gauge group and three quark-lepton generations. In some cases, mirror symmetry relates the models to other constructions used in phenomenological D-brane model building, like D-branes at singularities. Some simple N=1 supersymmetric configurations may lead to relatively tractable G_2 manifolds upon lift to M-theory, which would be non-compact but nevertheless yield four-dimensional chiral gauge field theories.

Supersymmetric Kaluza–Klein reductions of M-waves and MKK-monopoles

We investigate the Kaluza–Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza–Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza–Klein reductions by classifying the freely acting spacelike Killing vectors which preserve some Killing spinor. As a consequence we find a wealth of new supersymmetric IIA configurations involving composite and/or bound-state configurations of waves, D0 and D6-branes, Kaluza–Klein monopoles in type IIA and flux/nullbranes, and some other new configurations. Some new features raised by the geometry of the Taub–NUT space are discussed, namely the existence of reductions with no continuous moduli. We also propose an interpretation of the flux 5-brane in terms of the local description (close to the branes) of a bound state of D6-branes and ten-dimensional Kaluza–Klein monopoles.

Supersymmetric Configurations in Gauged Supergravity

We discuss supersymmetric configurations in gauged supergravity theories with particular emphasis on Euclidean D = 4, N = 4 gauged SU(2) × SU(1,1) supergravity.

An [formula omitted] supersymmetric G2-invariant flow in M-theory

It was found that deformation of S 7 gives rise to renormalization group (RG) flow from N=8 , SO(8)-invariant UV fixed point to N=1 , G 2-invariant IR fixed point in four-dimensional gauged N=8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G 2-invariant RG flow equations for both scalar fields and domain wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G 2-invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein–Maxwell equations. The nontrivial r (that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values makes the Einstein–Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional three-form gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein–Maxwell equations corresponding to the M-theory lift of the G 2-invariant RG flow.