Abstract: We study the effects of adding RR, NS and metric fluxes on a T^6/(\Omega (-1)^{F_L} I_3) Type IIA orientifold. By using the effective flux-induced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, whereas all can be stabilized in the AdS solutions. Many flux parameters are available which are unconstrained by RR tadpole cancellation conditions allowing to locate the minima at large volume and small dilaton. We also find that in AdS supersymmetric vacua with metric fluxes, the overall flux contribution to RR tadpoles can vanish or have opposite sign to that of D6-branes, allowing for new model-building possibilities. In particular, we construct the first N=1 supersymmetric intersecting D6-brane models with MSSM-like spectrum and with all closed string moduli stabilized. Some axion-like fields remain undetermined but they are precisely required to give Stuckelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the Freed-Witten anomaly guarantees that the axions with flux-induced masses are orthogonal to those giving masses to the U(1)'s. Cancellation of such anomalies also guarantees that the D6-branes in our N=1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry.

Abstract: We study the conditions to have supersymmetric D-branes on general = 1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3) × SU(3) structure on TM⊕TM, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Abstract: We study the conditions to have supersymmetric D-branes on general {\cal N}=1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3)\times SU(3) structure on T_M\oplus T^\star_M, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Abstract: We present the superconformal gauge theory living on the world-volume of D3 branes probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds Lp,q,r. Various checks of the identification are made by comparing the central charge and the R-charges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduced and the physics of the associated duality cascade discussed.

Abstract: We study the effects of adding RR, NS and metric fluxes on a T6/(Ω(−1)FLI3) type IIA orientifold. By using the effective flux-induced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, whereas all can be stabilized in the AdS solutions. Many flux parameters are available which are unconstrained by RR tadpole cancellation conditions allowing to locate the minima at large volume and small dilaton. We also find that in AdS supersymmetric vacua with metric fluxes, the overall flux contribution to RR tadpoles can vanish or have opposite sign to that of D6-branes, allowing for new model-building possibilities. In particular, we construct the first = 1 supersymmetric intersecting D6-brane models with MSSM-like spectrum and with all closed string moduli stabilized. Some axion-like fields remain undetermined but they are precisely required to give Stuckelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the Freed-Witten anomaly guarantees that the axions with flux-induced masses are orthogonal to those giving masses to the U(1)'s. Cancellation of such anomalies also guarantees that the D6-branes in our = 1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry.

Abstract: We motivate and apply a bottom-up approach to string phenomenology, which aims to construct the Standard Model as a decoupled world-volume theory on a D3-brane. As a concrete proposal for such a construction, we consider a single probe D3-brane on a partial resolution of a del Pezzo 8 singularity. The resulting world-volume theory reproduces the field content and interactions of the MSSM, however with a somewhat extended Higgs sector. An attractive feature of our approach is that the gauge and Yukawa couplings are dual to non-dynamical closed string modes, and are therefore tunable parameters.

Abstract: We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.

Abstract: We define the concept of Π-stability, a generalization of μ-stability of vector bundles, and argue that it characterizes = 1 supersymmetric brane configurations and BPS states in very general string theory compactifications with = 2 supersymmetry in four dimensions.

Abstract: In the past year, a new non-supersymmetric framework for electroweak symmetry breaking (with or without Higgs) involving SU(2)L × SU(2)R × U(1)B−L in higher dimensional warped geometry has been suggested. In this work, we embed this gauge structure into a GUT such as SO(10) or Pati–Salam. We showed recently (in hep-ph/0403143) that in a warped GUT, a stable Kaluza–Klein fermion can arise as a consequence of imposing proton stability. Here, we specify a complete realistic model where this particle is a weakly interacting right-handed neutrino, and present a detailed study of this new dark matter candidate, providing relic density and detection predictions. We discuss phenomenological aspects associated with the existence of other light () KK fermions (related to the neutrino), whose lightness is a direct consequence of the top quark's heaviness. The AdS/CFT interpretation of this construction is also presented. Most of our qualitative results do not depend on the nature of the breaking of the electroweak symmetry provided that it happens near the TeV brane.

Abstract: Four-dimensional supersymmetric SU(N) Yang-Mills theory on a sphere has highly charged baryon-like states built from anti-symmetric combinations of the adjoint scalars. We show that these states, which are equivalently described as holes in a free fermi sea of a reduced matrix model, are D-branes. Their excitations are stringlike and effectively realize Dirichlet and Neumann boundary conditions in various directions. The low energy brane dynamics should realize an emergent gauge theory that is local on a new space. We show that the Gauss' Law associated to this emergent gauge symmetry appears from combinatorial identities relating the stringy excitations. Although these excitations are not BPS, they can be near-BPS and we can hope to study them in perturbation theory. Accordingly, we show that the Chan-Paton factors expected for strings propagating on multiple branes arise dynamically, allowing the emergent gauge symmetry to be non-abelian.

Abstract: We study D7 brane probes holomorphically embedded in the Klebanov-Strassler model. Analyzing the κ-symmetry condition for D7 branes wrapping a 4-cycle of a deformed conifold we find configurations that do not break = 1 supersymmetry of the background. We compute the fluctuations of the probe around one of these configurations and obtain the spectrum of vector and scalar flavored mesons in the dual gauge theory. The spectrum is discrete and exhibits a mass gap.

Abstract: We examine low energy sparticle mass‐spectrum and electroweak symmetry breaking in the mixed modulus‐anomaly mediation which is naturally realized in KKLT flux compactification. We find that the anomaly‐mediation effectively lowers messenger scale in the moduli‐mediation and leads to ‘squeezed’ mass‐spectrum distinct from any known mediation mechanisms. The lightest neutralino typically becomes a mixed state of bino and higgsino or pure higgsino, which has a considerable impact on the cold dark matter physics.

Abstract: We carry out a thorough analysis of the moduli space of the cascading gauge theory found on p D3-branes and M wrapped D5-branes at the tip of the conifold. We find various mesonic branches of the moduli space whose string duals involve the warped deformed conifold with different numbers of mobile D3-branes. The branes that are not mobile form a BPS bound state at threshold. In the special case where p is divisible by M there also exists a one-dimensional baryonic branch whose family of supergravity duals, the resolved warped deformed conifolds, was constructed recently. The warped deformed conifold is a special case of these backgrounds where the resolution parameter vanishes and a Z_2 symmetry is restored. We study various brane probes on the resolved warped deformed conifolds, and successfully match the results with the gauge theory. In particular, we show that the radial potential for a D3-brane on this space varies slowly, suggesting a new model of D-brane inflation.

Abstract: In a simple reanalysis of the KKLMMT scenario, we argue that the slow roll condition in the D3-anti-D3-brane inflationary scenario in superstring theory requires no more than a moderate tuning. The cosmic string tension is very sensitive to the conformal coupling: with less fine-tuning, the cosmic string tension (as well as the ratio of tensor to scalar perturbation mode) increases rapidly and can easily saturate the present observational bound. In a multi-throat brane inflationary scenario, this feature substantially improves the chance of detecting and measuring the properties of the cosmic strings as a window to the superstring theory and our pre-inflationary universe.

Abstract: Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.

Abstract: We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T6/Z2, twelve of the sixteen zero modes originally present are lifted by the flux.

Abstract: We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type-IIB string theory. To this end, we derive the Dirac equation on a euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T-2/Z(2) orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.

Abstract: Inspired by the homological mirror symmetry conjecture of Kontsevich [30], we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth quasi– projective variety. MSC (2000): 18E30; 14J32.

Abstract: Recent type Ia supernovas data seemingly favor a dark energy model whose equation of state $w(z)$ crosses -1 very recently, which is a much more amazing problem than the acceleration of the universe. In this paper we show that it is possible to realize such a crossing without introducing any phantom component in a Gauss-Bonnet brane world with induced gravity, where a four dimensional curvature scalar on the brane and a five dimensional Gauss-Bonnet term in the bulk are present. In this realization, the Gauss-Bonnet term and the mass parameter in the bulk play a crucial role.

Abstract: We describe a new class of instanton effects in string compactifications that preserve only N=1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V, in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V. We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.

Abstract: We present a comparative analysis of localization of 4D gravity on a non 2 -symmetric scalar thick brane in both a 5-dimensional riemannian space time and a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincar? invariant thick brane solution which does not respect 2 -symmetry along the (non-)compact extra dimension. This field configuration reproduces the 2 -symmetric solutions previously found in the literature, in both the Riemann and the Weyl frames, when the parameter k 1 = 1. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y 0 . Thus, our field configurations can be compared with the standard Randall-Sundrum thin brane case. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the riemannian manifold turns out to be singular for the found solution, whereas its weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Sch?dinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Sch?dinger equation for the massless zero mode m 2 = 0 we obtain a single bound state which represents a stable 4-dimensional graviton in both frames. We also get a continuum gapless spectrum of KK states with positive 0$> m 2>0 that are suppressed at y 0 , turning into continuum plane wave modes as y approaches spatial infinity. We show that for the considered solution to our setup, the potential is always bounded and cannot adopt the form of a well with infinite walls; thus, we do not get a discrete spectrum of KK states, and we conclude that the claim that weylian structures mimic, classically, quantum behaviour does not constitute a generic feature of these geometric manifolds.

Abstract: We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.

Abstract: We study the Dirac equation on an M5 brane wrapped on a divisor in a Calabi-Yau fourfold in the presence of background flux. We reduce the computation of the normal bundle U(1) anomaly to counting the solutions of a finite-dimensional linear system on cohomology. This system depends on the choice of flux. In an example, we find that the presence of flux changes the anomaly and allows instanton corrections to the superpotential which would otherwise be absent.

Abstract: Holography relates the low energy regime of the five-dimensional description of generalized Randall–Sundrum cosmology to a four-dimensional theory. The four-dimensional theory describes observable matter interacting with a hidden (non-conformal) gauge theory. This provides a new arena for implementing the cosmological brane–bulk energy exchange processes studied previously. Unlike the five-dimensional description, there is no big-bang singularity in four dimensions. Some simple solutions are presented in four dimensions. A gauge theory description of observable four-dimensional gravity is also advocated.

Abstract: Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. In this context, we consider the hypothesis that this transition involves a quantum mechanical process. Our analysis is entirely analytical, with the objective of finding explicit mathematical expressions for the different quantum mechanical states and their cosmological implications. We employ a Friedmann-Robertson-Walker (FRW) minisuperspace model, characterized by two Lorentzian sectors, separated by a classically forbidden region. This is the configuration associated with the evolution of a generalized Chaplygin gas in a FRW universe. The Hartle-Hawking and Vilenkin wave functions are then computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, for specific initial conditions we found that the generalized Chaplygin gas parameters become related through an expression involving an integer $n$. We also introduce a phenomenological association between some brane-world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. The aim is to promote a discussion and subsequent research on the quantum creation of brane cosmologies from such a perspective. Additional results in this paper suggest that the brane tension would become related with the generalized Chaplygin gas parameters through another expression involving an integer.

Abstract: We quantize the moduli space of regular D1-D5 microstates, directly from Type IIB SUGRA. The moduli space is parametrized by a smooth closed non-selfintersecting curve in four dimensions, and we derive that the components of the curve satisfy chiral boson commutation relations, with the correct value of the effective Planck constant previously conjectured using U-duality. We use the Crnkovic-Witten-Zuckerman covariant quantization method, previously used to quantize the `bubbling AdS' geometries, combined with a certain new `consistency condition' which allows us to reduce the computation to quantizing perturbations around the plane wave.

Abstract: We present a comparative analysis of localization of 4D gravity on a non Z_2-symmetric scalar thick brane in both a 5-dimensional Riemannian space time and a pure geometric Weyl integrable manifold. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincare invariant thick brane solution which does not respect Z_2-symmetry along the (non-)compact extra dimension. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y_0. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the Riemannian manifold turns out to be singular for the found solution, whereas its Weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Schroedinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Schroedinger equation for the massless zero mode m^2=0 we obtain a single bound state which represents a stable 4-dimensional graviton in both frames. We also get a continuum gapless spectrum of KK states with positive m^2>0 that are suppressed at y_0, turning into continuum plane wave modes as "y" approaches spatial infinity. We show that for the considered solution to our setup, the potential is always bounded and cannot adopt the form of a well with infinite walls; thus, we do not get a discrete spectrum of KK states, and we conclude that the claim that Weylian structures mimic, classically, quantum behaviour does not constitute a generic feature of these geometric manifolds.