Flux vacua statistics for two‐parameter Calabi‐Yau's

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi‐Yau expressed as a hypersurface in WCP ⁴[1,1,2,2,6] by evaluating a suitable integral over the complex‐structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. In the process, we evaluate the periods near the conifold locus. We also study (non)supersymmetric solutions near the conifold locus, and show that supersymmetric solutions near the conifold locus do not support fluxes.     

D3 instantons in Calabi–Yau orientifolds with(out) fluxes

We investigate the instanton effects due to D3 branes wrapping a four-cycle in a Calabi–Yau orientifold with D7 branes. We study the condition for the nonzero superpotentials from the D3 instantons. To this aim we work out the zero mode structures of D3 branes wrapping a four-cycle both in the presence of the fluxes and in the absence of the fluxes. In the presence of the fluxes, the condition for the nonzero superpotential could be different from that without the fluxes. We explicitly work out a simple example of the orientifold of K3×T ²/Z ₂ with a suitable flux to show such behavior. The effects of the D3–D7 sectors are interesting and give further constraints for the nonzero superpotential. In a special configuration where D3 branes and D7 branes wrap the same four-cycle, multi-instanton calculus of D3 branes could be reduced to that of a suitable field theory. The structure of D5 instantons in Type I theory is briefly discussed.     

Compactifications of the heterotic string with unitary bundles

We describe a large new class of four‐dimensional supersymmetric string vacua defined as compactifications of the E₈ × E₈ and the SO(32) heterotic string on smooth Calabi‐Yau threefolds with unitary gauge bundles and heterotic five‐branes. The conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non‐flat line bundles into the ten‐dimensional gauge group, thus opening up the way for phenomenologically interesting string compactifications on simply connected manifolds. After a detailed analysis of the four‐dimensional effective theory we exemplify the general framework by means of a couple of explicit examples involving the spectral cover construction of stable holomorphic bundles. As for the SO(32) heterotic string, the resulting vacua can be viewed, in the S‐dual Type I picture, as a generalisation of magnetized D9/D5‐brane models. In the case of the E₈ × E₈ string, we find a natural way to construct realistic MSSM‐like models, either directly or via a flipped SU(5) GUT scenario.     

Type IIB orientifolds,D‐brane instantons and the LARGE volume scenario

This review article is concerned with three topics important for the construction of four‐dimensional models of particle physics in the context of type II String Theories. Special emphasis is put on a consistent presentation of these topics as well as on highlighting their interconnections. The first of the three topics deals with the tadpole cancellation conditions and the cancellation of chiral anomalies for type IIB orientifolds with orientifold three‐ and seven‐planes. The second topic is related to non‐perturbative effects originating from D‐brane instantons. In particular, in the presence of a realistic particle physics sector, a chiral zero‐mode constraint for contribution of instantons to the superpotential arises. The third topic is about moduli stabilisation in type IIB string compactifications. Two scenarios, the KKLT and Large Volume Scenario, are reviewed and a model for the latter scenario with the chiral zero‐mode constraint taken into account is presented.     

On the absence of large‐order divergences in superstring theory

The genus‐dependence of multi‐loop superstring amplitudes is estimated at large orders in perturbation theory using the super‐Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super‐modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N‐point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi‐Yau compactifications. The genus‐dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large‐order divergences in string perturbation theory, a result which is based only on the supersymmetric generalization of the Polyakov measure and not the gauge group of the string model.     

Massive tensor multiplets in N = 1 supersymmetry

We derive the action for a massive tensor multiplet coupled to chiral and vector multiplets as it can appear in orientifold compactifications of type IIB string theory. We compute the potential of the theory and show its consistency with the corresponding Kaluza‐Klein reduction of N = 1 orientifold compactifications. The potential contains an explicit mass term for the scalar in the tensor multiplet which does not arise from eliminating an auxiliary field. A dual action with an additional massive vector multiplet is derived at the level of superfields.     

Brane orbits

We complete the classification of half-supersymmetric branes in toroidally compactified IIA/IIB string theory in terms of representations of the T-duality group. As a by-product we derive a last wrapping rule for the space-filling branes. We find examples of T-duality representations of branes in lower dimensions, suggested by supergravity, of which none of the component branes follow from the reduction of any brane in ten-dimensional IIA/IIB string theory. We discuss the constraints on the charges of half-supersymmetric branes, determining the corresponding T-duality and U-duality orbits.     

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).     

D-brane solutions in a light-like linear dilaton background

The light-like linear dilaton background presents a simple time dependent solution of type II supergravity equations of motion that preserves 1/2 supersymmetry in ten dimensions. We construct supergravity D-brane solutions in a linear dilaton background starting from the known intersecting brane solutions in string theory. By applying a Penrose limit on the intersecting (NS1–NS5–NS5′)-brane solution, we find out a D5-brane in a linear dilaton background. We solve the Killing spinor equations for the brane solutions explicitly, and show that they preserve 1/4 supersymmetry. We also find a M5-brane solution in eleven-dimensional supergravity.     

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.     

Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in 𝒩 = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T⁶/Ω ℛ and the orbifolds T⁶/(ℤ_N × Ω ℛ) and T⁶/(ℤ₂ × ℤ_2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T⁶/ℤ₂ × ℤ₂ examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T⁶/ℤ₆^′T⁶/ℤ₆^′ from [2] are given.     

Topological phase transitions in Calabi‐Yau compactifications of M‐theory

In this thesis we construct five‐dimensional gauged supergravity actions which describe flop and conifold transitions in M‐theory compactified on Calabi‐Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2‐branes. After specifying the hypermultiplet sector the actions are uniquely determined by M‐theory. As an application we consider five‐dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space‐time.     

Hyper-Kähler manifolds and multiply intersecting branes

Generalized membrane solutions of D = 11 supergravity, for which the transverse space is a toric hyper-Kahler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D = 11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D = 11 solutions) can be mapped to solutions representing the intersection on a string of any number of D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we verify in a special case by a quaternionic extension of the analysis of Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8 supersymmetric solutions of orthogonally intersecting branes.     

Wilson line inflation

We present a general setup for inflation in string theory where the inflaton field corresponds to Wilson lines in compact space in the presence of magnetic fluxes. T-dualities and limits on the value of the magnetic fluxes relate this system to the standard D-brane inflation scenarios, such as brane-antibrane inflation, D3/D7 brane inflation and different configurations of branes at angles. This can then be seen as a generalised approach to inflation from open string modes. Inflation ends when the Wilson lines achieve a critical value and an open string mode becomes tachyonic. Then hybrid-like inflation, including its cosmic string remnants, is realized in string theory beyond the brane annihilation picture. Our formalism can be incorporated within flux-induced moduli stabilisation mechanisms in type IIB strings. Also, contrary to the standard D-brane separation, Wilson lines can be considered in heterotic string models. We provide explicit examples to illustrate similarities and differences of our mechanism to D-brane inflation. In particular we present an example in which the η problem present in brane inflation models is absent in our case. We have examples with both blue and red tilted spectral index and remnant cosmic string tension .     

D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the Z_N identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S³ part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.     

Evaporation of microscopic black holes in string theory and the bound on species

We address the question how string compactifications with D‐branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza‐Klein particles, both longitudinal and transversal to the D‐branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species‐counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentially growing number of Regge states does not preclude the existence of semi‐classical black holes of sub‐stringy size. Our analysis indicates that the effective number of string resonances to which such micro black holes evaporate is not exponentially large but is bounded by N = 1/g_s², which suggests the interpretation of the well‐known relation between the Planck and string scales as the saturation of the black hole bound on the species number. In addition, we also discuss some other issues in D‐brane compactifications with a low string scale of order TeV, such as the masses of light moduli fields.     

On the 4D effective theory in warped compactifications with fluxes and branes

We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.