Supersymmetry Breaking from a Calabi-Yau Singularity

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the $Y^{2,1}$ quiver gauge theory corresponding to a cone over the first del Pezzo surface, $dP_1$. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly-free fractional branes.Comment: 32 pages, 6 figures, latex, v2: minor changes, refs adde

Conformal Manifolds for the Conifold and other Toric Field Theories

In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this "conformal manifold". We identify the conformal manifold for all the Y^{p,q} toric singularities, paying special attention to the case of the conifold, Y^{1,0}. For a general Y^{p,q} the conformal manifold is three dimensional, while for the conifold it is five dimensional. There is always an exactly marginal deformation, analogous to the beta-deformation of N=4 SYM, which involves fluxes in the dual gravity description. This beta-deformation exists for any toric Calabi-Yau singularity.Comment: 30 pages, 5 figures; V2: References added, minor change

Orbits of Exceptional Groups, Duality and BPS States in String Theory

We give an invariant classification of orbits of the fundamental representations of exceptional groups $E_{7(7)}$ and $E_{6(6)}$ which classify BPS states in string and M theories toroidally compactified to d=4 and d=5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d=5 and d=4, respectively. The classification of BPS states preserving different numbers of supersymmetries is in close parallel to the classification of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 with symmetric space geometries are also classified including the exceptional N=2 theory that has $E_{7(-25)}$ and $E_{6(-26)}$ as its symmety in the respective dimensions.Comment: New references and two tables added, a new section on the orbits of N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 included and some minor changes were made in other sections. 17 pages. Latex fil

Lectures on Non-BPS Dirichlet branes

A comprehensive introduction to the boundary state approach to Dirichlet branes is given. Various examples of BPS and non-BPS Dirichlet branes are discussed. In particular, the non-BPS states in the duality of Type IIA on K3 and the heterotic string on T4 are analysed in detail.Comment: 46 pages, 5 figures, LaTeX; lectures given at the TMR network school on `Quantum aspects of gauge theories, supersymmetry and quantum gravity', Torino, 26 January - 2 February 2000, and at the `Spring workshop on Superstrings and related matters', Trieste, 27 March - 4 April 2000; references adde

Holographic dual of the Standard Model on the throat

We apply recent techniques to construct geometries, based on local Calabi-Yau manifolds, leading to warped throats with 3-form fluxes in string theory, with interesting structure at their bottom. We provide their holographic dual description in terms of RG flows for gauge theories with almost conformal duality cascades and infrared confinement. We describe a model of a throat with D-branes at its bottom, realizing a 3-family Standard Model like chiral sector. We provide the explicit holographic dual gauge theory RG flow, and describe the appearance of the SM degrees of freedom after confinement. As a second application, we describe throats within throats, namely warped throats with discontinuous warp factor in different regions of the radial coordinate, and discuss possible model building applications.Comment: 46 pages, 21 figures, reference adde

Dibaryons from Exceptional Collections

We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface without any Weyl group ambiguity. As one application of the correspondence, we identify the cubic anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N superconformal gauge theories. Examples can be given for all del Pezzo surfaces using three- and four-block exceptional collections. Markov-type equations enforce consistency among anomaly equations for three-block collections.Comment: 47 pages, 11 figures, corrected ref

D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics

We discuss general properties of D-brane model building at toric singularities. Using dimer techniques to obtain the gauge theory from the structure of the singularity, we extract results on the matter sector and superpotential of the corresponding gauge theory. We show that the number of families in toric phases is always less than or equal to three, with a unique exception being the zeroth Hirzebruch surface. With the physical input of three generations we find that the lightest family of quarks is massless and the masses of the other two can be hierarchically separated. We compute the CKM matrix for explicit models in this setting and find the singularities possess sufficient structure to allow for realistic mixing between generations and CP violation.Comment: 55 pages, v2: typos corrected, minor comments adde

Multi-flux warped throats and cascading gauge theories

We describe duality cascades and their infrared behavior for systems of D3-branes at singularities given by complex cones over del Pezzo surfaces (and related examples), in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. This implies that for the dual supergravity viewpoint, the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed warped throat solutions with 3-form fluxes, describing the cascading RG flow of the gauge theory. This behavior thus generalizes the Klebanov-Strassler deformation of the conifold. We describe several explicit examples, including models with several scales of strong gauge dynamics. In the regime of widely separated scales, the dual supergravity solutions should correspond to throats with several radial regions with different exponential warp factors. These rich throat geometries are expected to have interesting applications in compactification and model building. Along our studies, we also construct explicit duality cascades for gauge theories with irrational R-charges, obtained from D-branes probing complex cones over dP1 and dP2