Sebastian Franco

D = 4 chiral string compactifications from intersecting branes

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...

Gauge theories from toric geometry and brane tilings

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the Suspended Pinch Point.

An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals.

We describe an infinite family of quiver gauge theories that are AdS/CFT dual to a corresponding class of explicit horizon Sasaki-Einstein manifolds. The quivers may be obtained from a family of orbifold theories by a simple iterative procedure. A key aspect in their construction relies on the global symmetry which is dual to the isometry of the manifolds. For an arbitrary such quiver we compute the exact R-charges of the fields in the IR by applying a-maximization. The values we obtain are generically quadratic irrational numbers and agree perfectly with the central charges and baryon charges computed from the family of metrics using the AdS/CFT correspondence. These results open the way for a systematic study of the quiver gauge theories and their dual geometries.

Metastable vacua and D-branes at the conifold

We consider quiver gauge theories arising on D-branes at simple Calabi-Yau singularities (quotients of the conifold). These theories have metastable supersymmetry breaking vacua. The field theoretic mechanism is basically the one exhibited by the examples of Intriligator, Seiberg and Shih in SUSY QCD. In a dual description, the SUSY breaking is captured by the presence of anti-branes. In comparison to our earlier related work, the main improvements of the present construction are that we can reach the free magnetic range of the SUSY QCD theory where the existence of the metastable vacua is on firm footing, and we can see explicitly how the small masses for the quark flavors (necessary to the existence of the SUSY breaking vacua) are dynamically stabilized. One crucial mass term is generated by a stringy instanton. Finally, our models naturally incorporate R-symmetry breaking in the non-supersymmetric vacuum, in a way similar to the examples of Kitano, Ooguri and Ookouchi.

Dynamical SUSY breaking at meta-stable minima from D-branes at obstructed geometries

We study the existence of long-lived meta-stable supersymmetry breaking vacua in gauge theories with massless quarks, upon the addition of extra massive flavors. A simple realization is provided by a modified version of SQCD with Nf,0 < Nc massless flavors, Nf,1 massive flavors and additional singlet chiral fields. This theory has local meta-stable minima separated from a runaway behavior at infinity by a potential barrier. We find further examples of such meta-stable minima in flavored versions of quiver gauge theories on fractional branes at singularities with obstructed complex deformations, and study the case of the dP1 theory in detail. Finally, we provide an explicit String Theory construction of such theories. The additional flavors arise from D7-branes on non-compact 4-cycles of the singularity, for which we find a new efficient description using dimer techniques.

Fractional branes and dynamical supersymmetry breaking

We study the dynamics of fractional branes at toric singularities, including cones over del Pezzo surfaces and the recently constructed Y p,q theories. We find that generically the field theories on such fractional branes show dynamical supersymmetry breaking, due to the appearance of non-perturbative superpotentials. In special cases, one recovers the known cases of supersymmetric infrared behaviors, associated to SYM confinement (mapped to complex deformations of the dual geometries, in the gauge/string correspondence sense) or N = 2 fractional branes. In the supersymmetry breaking cases, when the dynamics of closed string moduli at the singularity is included, the theories show a runaway behavior (involving moduli such as FI terms or equivalently dibaryonic operators), rather than stable non-supersymmetric minima. We comment on the implications of this gauge theory behavior for the infrared smoothing of the dual warped throat solutions with 3-form fluxes, describing duality cascades ending in such field theories. We finally provide a description of the different fractional branes in the recently introduced brane tiling configurations.

Towards M2-brane Theories for Generic Toric Singularities

We construct several examples of (2+1) dimensional = 2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is the gauge theory associated with the cone over Q111. For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models. Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.

Non-supersymmetric meta-stable vacua from brane configurations

We construct configurations of NS-, D4-, and D6-branes in type IIA string theory, realizing the recently discussed non-supersymmetric meta-stable minimum of 4d = 1 SU(Nc) super-Yang-Mills theories with massive flavors. We discuss their lift to M-theory and the mechanism of pseudo-moduli stabilization. We extend the construction to many other examples of meta-stable minima, including the SO/Sp theories, SU(Nc) with matter in two-index tensor representations, and to a chiral gauge theory.

Unhiggsing the del Pezzo

We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for blowups of geometries whose gauge theory data are known. As specific applications we unhiggs the well-studied theories for the cone over the third del Pezzo surface. We arrive at what we call pseudo del Pezzos and these will constitute a first step toward the understanding of higher, non toric del Pezzos. Moreover, our methods and results give further support for toric duality as well as obtaining superpotentials from global symmetry considerations.

Dimers and orientifolds

We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories known so far. Furthermore, new orientifolds of non-orbifold toric singularities are obtained. The possible applications of the tools presented in this paper are diverse. One particular application is the construction of models which feature dynamical supersymmetry breaking as well as the computation of D-instanton induced superpotential terms.