Abstract: We consider certain supersymmetric configurations of intersecting branes and branes ending on branes and analyze the duality between their open and closed string interpretation. The examples we study are chosen such that we have the lower dimensional brane realizing an n+1 dimensional conformal field theory on its worldvolume and the higher dimensional one introducing a conformal boundary. We also consider two CFTs, possibly with different central charges, interacting along a common conformal boundary. We show with a probe calculation that the dual closed string description is in terms of gravity in an AdS_{n+2} bulk with an AdS_{n+1} defect or two different AdS_{n+2} spaces joined along a defect. We also comment briefly on the expected back-reaction.

Abstract: We study the fluctuation spectrum of linearized gravity around non-fine-tuned branes. We focus on the case of an AdS4 brane in AdS5. In this case, for small cosmological constant, the warp factor near the brane is essentially that of a Minkowski brane. However, far from the brane, the metric differs substantially. The space includes the AdS5 boundary, so it has infinite volume. Nonetheless, for sufficiently small AdS4 cosmological constant, there is a bound state graviton in the theory, and four-dimensional gravity is reproduced. However, it is a massive bound state that plays the role of the four-dimensional graviton.

Abstract: Theoretical studies on more than three spatial dimensions are currently showing a distinct shift toward the 'brane world' picture, in which ordinary matter (with the possible exceptions of gravitons and hypothetical particles interacting very weakly with matter) is within a three-dimensional submanifold — brane — embedded in a multi-dimensional space. The extra dimensions may be large and indeed infinite and may show up directly in current or future experiments. In the present paper the basic ideas of the brane theory are presented in an accessible way using simple field-theoretical models.

Abstract: We construct the first three family N = 1 supersymmetric string model with standard model gauge group SU(3)(C) x SU(2)(L) x U(1)(Y) from an orientifold of type IIA theory on T(6)/(Z(2) x Z(2)) and D6-branes intersecting at angles. In addition to the minimal supersymmetric standard model particles, the model contains right-handed neutrinos, a chiral (but anomaly-free) set of exotic multiplets, and extra vectorlike multiplets. We discuss some phenomenological features of this model.

Abstract: We show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the supersymmetry preserving branes at any point in CY moduli space, completing the proposal of II-stability.

Abstract: Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on nontrivial n-cycles on T2n×(R2(3−n)/ZN), for n=1, 2, 3. The gauge theories on the four noncompact dimensions of the brane world-volume are generically chiral and nonsupersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a Green–Schwarz mechanism mediated by RR partners of untwisted and/or twisted moduli. This class of models is of potential phenomenological interest, and we construct explicit examples of SU(3)×SU(2)×U(1) three-generation models. The models are nonsupersymmetric, but the string scale may be lowered close to the weak scale so that the standard hierarchy problem is avoided. We also comment on the presence of scalar tachyons and p...

Abstract: We investigate the charged Schwarzschild-Anti-deSitter (SAdS) BH thermodynamics in 5d Einstein-Gauss-Bonnet gravity with electromagnetic field. The Hawking-Page phase transitions between SAdS BH and pure AdS space are studied. The corresponding phase diagrams (with critical line defined by GB term coefficient and electric charge) are drawn. The possibility to account for higher derivative Maxwell terms is mentioned. In frames of proposed dS/CFT correspondence it is demonstrated that brane gravity maybe localized similarly to AdS/CFT. SdS BH thermodynamics in 5d Einstein and Einstein-Gauss-Bonnet gravity is considered. The corresponding (complicated) surface counterterms are found and used to get the conserved BH mass, free energy and entropy. The interesting feature of of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. We speculate that the appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur.

Abstract: We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C-(p) (p = 0, 1,..., 9) as the effective field theory of type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p less than or equal to 3 or p greater than or equal to 5, which allows us to write a new bulk action that can be coupled to N = 1 supersymmetric brane actions. The case of eight-braves is studied in detail using the new bulk & brane action. The supersymmetric negative-tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and O8-planes are fundamental in type I' string theory. A BPS eight-brave solution is given which satisfies the jump conditions on the wall. It implies a quantization of the mass parameter in string units. Also, we find a maximal distance between the two walls, depending on the string coupling and the mass parameter. We derive the same results via supersymmetric flow equations.

Abstract: We present what we believe are the first specific string (D-brane) constructions whose low-energy limit yields just a three generation $SU(3)\times SU(2)\times U(1)$ standard model with no extra fermions nor U(1)'s (without any further effective field theory assumption). In these constructions the number of generations is given by the number of colours. The Baryon, Lepton and Peccei-Quinn symmetries are necessarily gauged and their anomalies cancelled by a generalized Green-Schwarz mechanism. The corresponding gauge bosons become massive but their presence guarantees automatically proton stability. There are necessarily three right-handed neutrinos and neutrino masses can only be of Dirac type. They are naturally small as a consequence of a PQ-like symmetry. There is a Higgs sector which is somewhat similar to that of the MSSM and the scalar potential parameters have a geometric interpretation in terms of brane distances and intersection angles. Some other physical implications of these constructions are discussed.

Abstract: Chiral fermions naturally appear at intersections of branes at angles. We propose a string scenario in which different SM gauge interactions propagate on different (intersecting) brane worlds, partially wrapped in the extra dimensions. Quarks and leptons live at brane intersections, located at different positions in the extra dimensions. Replication of families follows because branes generically intersect at several points. Gauge and Yukawa couplings can be computed in terms of the compactification radii. Yukawa couplings are hierarchical, proportional to exp −A, where A is the area of a string world-sheet extending among three intersections. The models are non-supersymmetric but the string scale may be lowered down to 1-10 TeV. The proton is however stable due to discrete symmetries, exact in perturbation theory. The scenario has KK, winding and other new excited states (`gonions'), with masses below the string scale and accessible to accelerators. The models contain scalar tachyons with the quantum numbers of SM Higgs doublets, and we propose that they induce electroweak symmetry breaking in a novel way. We present specific string models with the above properties, built from D4-branes wrapping on T2 × (T2)2/N, and leading to 3-family semirealistic spectra.

Abstract: We analyze the perturbative stability of non-supersymmetric intersecting brane world models on tori. Besides the dilaton tadpole, a dynamical instability in the complex structure moduli space occurs at string disc level, which drives the background geometry to a degenerate limit. We show that in certain orbifold models this latter instability is absent as the relevant moduli are frozen. We construct explicit examples of such orbifold intersecting brane world models and discuss the phenomenological implications of a three generation Standard Model which descends naturally from an SU(5) GUT theory. It turns out that various phenomenological issues require the string scale to be at least of the order of the GUT scale. As a major difference compared to the Standard Model, some of the Yukawa couplings are excluded so that the standard electroweak Higgs mechanism with a fundamental Higgs scalar is not realized in this set-up.

Abstract: In this paper we give the boundary string field theory description of brane-antibrane systems. From the world-sheet action of brane-antibrane systems we obtain the tachyon potential and discuss the tachyon condensation exactly. We also find the world-volume action including the gauge fields. Moreover we determine RR-couplings exactly for non-BPS branes and brane-antibranes. These couplings are written by superconnections and correspond to K1(M) and K0(M) for the non-BPS branes and brane-antibranes, respectively. We also show that Myers terms appear if we include the transverse scalars in the boundary sigma model action.

Abstract: We present non-supersymmetric toroidal compactifications of type-I string theory with both constant background NSNS two-form flux and non-trivial magnetic flux on the various D9-branes. The non-vanishing B-flux admits four-dimensional models with three generations of chiral fermions in standard model like gauge groups. Additionally, we consider the orbifold 4/2, again with both kinds of background flux present, leading to non-supersymmetric as well as supersymmetric models in six dimensions. All models have T-dual descriptions as intersecting brane worlds.

Abstract: We investigate supersymmetric SU(5) grand-unified theories (GUTs) realized in 5 space-time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S^1/(Z_2 x Z_2') orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane. Although this model does not unify the MSSM matter within SU(5) multiplets, it explains gauge coupling unification. A second model with MSSM matter in the SU(5)-symmetric bulk preserves both the SU(5) explanation of fermion quantum numbers as well as gauge-coupling unification. Both models naturally avoid problematic SU(5) predictions for the Yukawa couplings of the first two generations and are consistent with proton decay constraints. We analyse the running of gauge couplings above the compactification scale in terms of a 5d effective action and derive the implications for the values of compactification scale, unification scale and of the scale at which the bulk gauge theory becomes strongly coupled.

Abstract: We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C^(p) (p=0,1,...,9) as the effective field theory of Type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p =5 which allows us to write a new bulk action that can be coupled to N=1 supersymmetric brane actions. The case of 8-branes is studied in detail using the new bulk & brane action. The supersymmetric negative tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and O8-planes are fundamental in Type I' string theory. A BPS 8-brane solution is given which satisfies the jump conditions on the wall. It implies a quantization of the mass parameter in string units. Also we find a maximal distance between the two walls, depending on the string coupling and the mass parameter. We derive the same results via supersymmetric flow equations.

Abstract: This is a write-up of introductory lectures on black holes in string theory given at TASI-99. Topics discussed include: Black holes, thermodynamics and the Bekenstein-Hawking entropy, the information problem; supergravity actions, conserved quantum numbers, supersymmetry and BPS states, units and duality, dimensional reduction, solution-generating; extremal M-branes and D-branes, smearing, probe actions, nonextremal branes, the Gregory-Laflamme instability; breakdown of supergravity and the Correspondence Principle, limits in parameter space, singularity resolution; making black holes with branes, intersection-ology, explicit d=5,4 examples; string/brane computations of extremal black hole entropy in d=5,4, rotation, fractionation; non-extremality and entropy, the link to BTZ black holes, Hawking radiation and absorption cross-sections in the string/brane and supergravity pictures.

Abstract: A general model of multidimensional ${R}^{2}$ gravity including a Riemann tensor square term (nonzero c case) is considered. The number of brane-worlds in such a model is constructed (mainly in five dimensions) and their properties are discussed. The thermodynamics of a Schwarzschild--anti-deSitter (S-AdS) BH (with boundary) is presented when perturbation on c is used. The entropy, free energy, and energy are calculated. For a nonzero c the entropy (energy) is not proportional to the area (mass). The equation of motion of the brane in a BH background is presented as a FRW equation. Using a dual CFT description it is shown that the dual field theory is not a conformal one when c is not zero. In this case the holographic entropy does not coincide with the BH entropy (they coincide for Einstein gravity or $c=0$ HD gravity where the AdS/CFT description is well applied). An asymmetrically warped background (an analogue of a charged AdS BH) where Lorentz invariance violation occurs is found. The cosmological 4D dS brane connecting two dS bulk spaces is formulated in terms of the parameters of ${R}^{2}$ gravity. Within the proposed dS/CFT correspondence the holographic conformal anomaly from five-dimensional higher derivative gravity in a de Sitter background is evaluated.

Abstract: We discuss a calculable version of brane inflation, in which a set of parallel D-brane and anti-D-brane worlds, initially displaced in extra dimension, slowly attract each other In the effective four-dimensional theory this slow motion of branes translates into a slow-roll of a scalar field (proportional to their separation) with a flat potential that drives inflation The number of possible e-foldings is severely constrained The scalar spectral index is found to be 097, while the effective compactification scale is of order $10^{12}$ GeV Reheating of the Universe is provided by collision and subsequent annihilation of branes

Abstract: In this paper we propose a new mechanism of inflating the Universe with non-BPS $D4$ branes which decay into stable $D3$ branes via tachyon condensation. In a single brane scenario the tachyon potential is very steep and unable to support inflation. However if the universe lives in a stack of branes produced by a set of non-interacting unstable $\tilde {D4}$ branes, then the associated set of tachyons may drive inflation along our 3 spatial dimensions. After tachyon condensation the Universe is imagined to be filled with a set of parallel stable $D3$ branes. We study the scalar density perturbations and reheating within this setup.

Abstract: We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.

Abstract: We discuss the discrete k D-brane charges (twisted K-theory charges) in five-brane backgrounds from several different points of view. In particular, we interpret it as a result of a standard Higgs mechanism. We show that certain degrees of freedom (singletons) on the boundary of space can extend the corresponding k symmetry to U(1). Related ideas clarify the role of AdS singletons in the AdS/CFT correspondence.

Abstract: We investigate solutions of type II supergravity which have the product R 1,3 ×M 6 structure with non-compact M 6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N = 1 supersymmetric ‘NS5-brane wrapped on a 2-sphere’ solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the K¨ ahler and parallel (3, 0)-forms of the corresponding M 6 . In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of the underlying type II theory. We also demonstrate that the ordinary and fractional D3-brane (5-brane wrapped on a 2-cycle) solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields, i.e. from a single one-dimensional action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5brane on a 2-sphere background can be found as a solution of a first-order system following from a superpotential.

Abstract: We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.