Intersecting M-branes

We present the magnetic duals of Güven's electric-type solutions of D = 11 supergravity preserving 1/4 or 1/8 of the D = 11 supersymmetry. We interpret the electric solutions as n orthogonal intersecting membranes and the magnetic solutions as n orthogonal intersecting 5-branes, with n = 2, 3; these cases obey the general rule that p-branes can self-intersect on (p − 2)-branes. On reduction to D = 4 these solutions become electric or magnetic dilaton black holes with dilaton coupling constant a = 1 (for n = 2) or (for n = 3). We also discuss the reduction to D = 10.     

D-branes and T-duality

We show how the T-duality between D-branes is realized (i) on p-brane solutions (p = 0,…,9) of IIA/IIB supergravity and (ii) on the D-brane actions (p = 0,…, 3) that act as source terms for the p-brane solutions. We point out that the presence of a cosmological constant in the IIA theory leads, by the requirement of gauge invariance, to a topological mass term for the worldvolume gauge field in the 2-brane case.     

Dyonic membranes

We present dyonic multi-membrane solutions of the N = 2 D = 8 supergravity theory that serves as the effective field theory of the T²-compactified type II superstring theory. The ‘electric’ charge is fractional for generic asymptotic values of an axion field, as for D = 4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an subgroup of the type II D = 8 T-duality group, and are non-singular when considered as solutions of T³-compactified D = 11 supergravity. On K₃ compactification to D = 4, the conjectured type II/heterotic equivalence allows the group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of K₃ as S-duals of perturbative heterotic string states.     

Overlapping branes in M-theory

We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2⁻ⁿ of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string.     

Towards a naturally small cosmological constant from branes in 6D supergravity

We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r⁴ when compactified on two dimensions having Kaluza–Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of non-supersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in sub-millimeter tests of gravity and at the Large Hadron Collider. We do find self-tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam–Sezgin gauged 6D supergravity compactified on a 2-sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.     

Super p-branes

It is shown that the extension of the spacetime supersymmetric Green-Schwarz covariant action p-dimensional extended objects (p-branes) is possible if and only if the on-shell p-dimensional Bose and Fermi degrees of freedom are equal. This is further evidence for world-tube supersymmetry in these models. All the p-branes models are related to superstring actions in d=3, 4, 6 or 10 dimensions by double dimensional reduction (which we generalise to reduction on arbitrary compact spaces), and we also show how they may be considered as topological defects of supergravity theories.     

Supersymmetry breaking with vanishing F-terms in supergravity theories

In conventional supergravity theories, supersymmetry is broken by a non-zero F-term, and the cosmological constant is fine tuned to zero by a constant in the superpotential W. We discuss a class of supergravity theories with vanishing F-terms but W ≠ 0 being generated dynamically. The cosmological constant is assumed to be cancelled by a non-zero D-term. In this scenario the gravity-mediated soft masses depend only on a single parameter, the gravitino mass. They are automatically universal, independently of the Kähler metric, and real. Thus, dangerous flavor or CP violating interactions are suppressed. Unlike in conventional supergravity models, the Polonyi problem does not arise.     

Supersymmetric 3D anti-de Sitter space solutions of type IIB supergravity

For every positively curved K?hler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.     

Effective actions of intersecting brane worlds, fluxes and gaugino condensation

In this article we will first discuss the construction of brane world models being built either by intersecting D6-branes in type IIA orientifolds or, in the T-dual mirror picture, by D3- plus D7-branes with f-flux in type IIB orientifolds. We will show how their effective action is obtained by the calculation of scattering amplitudes between open and closed string states on intersecting D6-branes respectively on D3- and D7-branes. Secondly, turning on type IIB 3-form fluxes we will compute the induced soft supersymmetry breaking terms for the matter fields, like gaugino and scalar field masses. Finally, we will discuss the generation of 3-form flux in type IIB supergravity, which can be associated to the dynamical formation of a gaugino condensate in the confining phase of the dual N=1^* gauge theory. To cite this article: D. Lüst, C. R. Physique 5 (2004).

Résumé

Dans cet article nous discutons tout d'abord la construction de modèles de monde branaires construits soit par intersection de branes D6 dans des orientifolds de type IIA ou, dans la représentation T-duale, par des branes de type D3 et D7 avec des flux f dans les orientifolds de type IIB. Nous montrons comment obtenir leurs actions effectives en calculant les amplitudes de diffusion sur des intersections de branes de D6 et aussi sur des branes de type D3 et D7. Ensuite, nous allumons des flux pour la 3-forme de type IIB et nous calculons les termes de brisure douce de la supersymétrie pour les champs de matière, comme les masses du jaugino et des champs scalaires. Enfin, nous discutons la génération de flux pour la 3-forme de type IIB en supergravité, qui peut-être associée à la dynamique de la formation de condensat de jaugino dans la phase confinante de la théorie de jauge duale N=1^*. Pour citer cet article : D. Lüst, C. R. Physique 5 (2004).     

Thermodynamics of spinning D3-branes

Spinning black 3-branes in type IIB supergravity are thermodynamically stable up to a critical value of the angular momentum density. Inside the region of thermodynamic stability, the free energy from supergravity is roughly reproduced by a naive model based on free N = 4 super-Yang-Mills theory on the world-volume. The field theory model correctly predicts a limit on angular momentum density, but near this limit it does not reproduce the critical exponents one can compute from supergravity. Analogies with Bose condensation and modified matrix models are discussed, and a mean field theory improvement of the naive model is suggested which corrects the critical exponents.     

A new solution of d = 11 supergravity with internal isometry group SU(3) × SU(2) × U(1)

A new solution of the bosonic sector of D = 11 supergravity is presented in which the internal space has the topology CP² × S² × S¹ and the internal isometry group is SU(3) × SU(2) × U(1).     

Vector multiplets coupled to N=2 supergravity: Super-Higgs effect, flat potentials and geometric structure

We obtain general properties of N=2 gauged extended supergravity coupled to vector multiplets, which can gauge an arbitrary group. General formulas for masses and curvatures are derived. Particular attention is devoted to the scalar potential of the theory which determines the classical vacuum structure. Explicit examples are given in which the potential is identically zero, but supersymmetry is broken. It is found that these theories are symmetric under generalized duality transformations.     

Supermembranes

An example is given of the spontaneous breaking of D = 4, N = 2 global supersymmetry down to N = 1. The example is a four-dimensional membrane in a six-dimensional supersymmetric gauge theory. The effective low-energy action for the membrane is a generalization of the Green—Schwarz covariant action.     

Quantum discontinuity for massive spin-3/2 with a Λ term

We show that the recently demonstrated absence of the van Dam–Veltman–Zakharov discontinuity for massive spin-3/2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop. As a numerical check on the calculation, we rederive the vanishing of the one-loop beta function for D=11 supergravity on AdS₄×S⁷ level-by-level in the Kaluza–Klein tower.     

Chiral supersymmetric pp-wave solutions of IIA supergravity

We describe solutions of type IIA (N = 2, D = 10) supergravity built under the assumption of the existence of at least one residual chiral supersymmetry. Their geometry is of pp-wave type. Explicit parametrization of the metric and matter field components, in terms of Killing spinors and arbitrary functions, is provided.     

Scaling properties of resonant electron transfer in ion—metal-surface interactions

Scaling properties of resonant electron transfer in the interaction of atoms and positive ions with metal surfaces are revealed by examining the dependence of numerically calculated transition matrix elements and (first-order) transition rates upon the scaled ion-surface distance D = D/D_n, where D_n is the classical threshold distance for electron transfer involving ionic stat principal quantum number n. For zero orbital angular momentum and fixed energy of the ionic states, the n-dependence of the rates at D = 1 is found to approach, in the large-n limit, a simple power law. A scaling law is established that connects, in the range D 1, transition rates for arbitrary (large) principal quantum numbers.     

Domain-wall supergravities from sphere reduction

Kaluza-Klein sphere reductions of supergravities that admit Ads × Sphere vacuum solutions are believed to be consistent. The examples include the S⁴ and S⁷ reductions of eleven-dimensional supergravity, and the S⁵ reduction of ten-dimensional type IIB supergravity . In this paper we provide evidence that sphere reductions of supergravities that admit instead Domain-wallxSphere vacuum solutions are also consistent, where the background can be viewed as the near-horizon structure of a dilatonic p-brane of the theory. The resulting lower-dimensional theory is a gauged supergravity that admits a domain wall, rather than AdS, as a vacuum solution. We illustrate this consistency by taking the singular limits of certain modulus parameters, for which the originalSⁿ compactifying spheres (n = 4, 5 or 7) becomes S^p × R^q, with p = n − q < n. The consistency of the S⁴, S⁷ reductions then implies the consistency of the ^Sp reductions of the lower-dimensional supergravities. In particular, we obtain explicit non-linear ansätze for the S³ reduction of type IIA and heterotic supergravities, restricting to the U(1)² subgroup of the SO(4) gauge group of S³. We also study the black-hole solutions in the lower-dimensional gauged supergravities with domain-wall backgrounds. We find new domain-wall black holes which are not the singular-modulus limits of the AdS black holes of the original theories, and we obtain their Killing spinors.     

The effective action of D‐branes in Calabi‐Yau orientifold compactifications

In this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.     

Algebraic derivation of N = 2 supergravity constraints

A purely algebraic derivation is given of the superspace constraints of N = 2 extended supergravity. The derivation proceeds through an analysis of the integrability conditions needed to preserve the irreducible representations of rigid N = 2 supersymmetry, taking account of the local complex dilation and SU(2) invariances of the constraints.     

Scattering of several multiply charged extremal D = 5 black holes

The moduli space metric for an arbitrary number of extremal D = 5 black holes with arbitrary relatively supersymmetric charges is found.