Box Graphs and Singular Fibers

We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as `flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E_6, E_7 and E_8.Comment: 107 pages, 44 figures, v2: added case of E7 monodromy-reduced fiber

Compact F-theory GUTs with U(1)_PQ

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level \mu term, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.Comment: 73 pages, 5 figures, v2: minor corrections to 4.3 and 6.3.1, reference adde

An Instanton Toolbox for F-Theory Model Building

Several dimensionful parameters needed for model building can be engineered in a certain class of SU(5) F-theory GUTs by adding extra singlet fields which are localized along pairwise intersections of D7-branes. The values of these parameters, however, depend on dynamics external to the GUT which causes the singlets to acquire suitable masses or expectation values. In this note, we demonstrate that D3-instantons which wrap the same 4-cycle as one of the intersecting D7's can provide precisely the needed dynamics to generate several important scales, including the supersymmetry-breaking scale and the right-handed neutrino mass. Furthermore, these instantons seem unable to directly generate the \mu term suggesting that, at least in this class of models, it should perhaps be tied to one of the other scales in the problem. More specifically, we study the simple system consisting of a pair of D7-branes wrapping del Pezzo surfaces which intersect along a curve $\Sigma$ of genus 0 or 1 and classify all instanton configurations which can potentially contribute to the superpotential. This allows one to formulate topological conditions which must be imposed on \Sigma for various model-building applications. Along the way, we also observe that the construction of arXiv:0808.1286 which engineers a linear superpotential in fact realizes an O'Raifeartaigh model at the KK scale whose 1-loop Coleman-Weinberg potential generically leads to a metastable, long-lived SUSY-breaking vacuum.Comment: 18 pages, 2 figures; v2: updated to reflect corrections in v2 of 0808.128

F-theory Compactifications for Supersymmetric GUTs

We construct a family of elliptically fibered Calabi-Yau four-folds Y_4 for F-theory compactifications that realize SU(5) GUTs in the low-energy limit. The three-fold base X_3 of these fibrations is almost Fano and satisfies the topological criteria required to ensure that the U(1)_Y gauge boson remains massless, while allowing a decoupling of GUT and Planck scale physics. We study generic features of these models and the ability to engineer three chiral generations of MSSM matter. Finally, we demonstrate that it is relatively easy to implement the topological conditions required to reproduce certain successful features of local F-theory models, such as the emergence of flavor hierarchies.Comment: 55 pages, 10 figure

Theories of Class F and Anomalies

We consider the 6d (2,0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-duality transformations. These monodromies occur around 2d loci in space-time, the duality defects, above which the fiber is singular. The key role that the fibration plays here motivates refering to this setup as theories of class F. In the simplest instance this gives rise to 4d N=4 Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z) monodromies. We determine the anomaly polynomial for these theories by pushing forward the anomaly polynomial of the 6d (2,0) theory along the fiber. This gives rise to corrections to the anomaly polynomials of 4d N=4 SYM and theories of class S. For the torus case, this analysis is complemented with a field theoretic derivation of a U(1) anomaly in 4d N=4 SYM. The corresponding anomaly polynomial is tested against known expressions of anomalies for wrapped D3-branes with varying coupling, which are known field theoretically and from holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories with varying coupling, are also discussed.Comment: 54 pages, 1 figure, v2: added discussion of non-supersymmetric extension, v3: version as appears in JHE

Unification and Phenomenology of F-Theory GUTs with U(1)_PQ

We undertake a phenomenological study of SU(5) F-theory GUT models with an additional U(1)_{PQ} symmetry. In such models, breaking SU(5) with hypercharge flux leads to the presence of non-GUT multiplets in the spectrum. We study the effect these have on the unification of gauge couplings, including two-loop running as well as low- and high-scale threshold corrections. We use the requirement of unification to constrain the size of thresholds from KK modes of SU(5) gauge and matter fields. Assuming the non-GUT multiplets play the role of messengers of gauge mediation leads to controlled non-universalities in the sparticle spectrum while maintaining grand unification, and we study the LHC phenomenology of this scenario. We find that the MSSM spectrum may become compressed or stretched out {by up to a factor of three} depending on the distribution of hypercharge flux. We present a set of benchmark points whose production cross-sections and decays we investigate, and argue that precision kinematic edge measurements will allow the LHC to distinguish between our model and mGMSB.Comment: 46 pages, 15 figure

Expression of Y-box-binding protein dbpC/contrin, a potentially new cancer/testis antigen

Y-box-binding proteins are members of the human cold-shock domain protein superfamily, which includes dbpA, dbpB/YB-1, and dbpC/contrin. dbpC/contrin is a germ cell-specific Y-box-binding protein and is suggested to function as a nuclear transcription factor and RNA-binding protein in the cytoplasm. Whereas ubiquitous dbpB/YB-1 expression has been well studied in various types of human carcinomas as a prognostic or predictive marker, the dbpC/contrin expression in human tumour cells has not been reported. In this report, we provide the first evidence showing that dbpC was highly expressed in human testicular seminoma and ovarian dysgerminomas, and in carcinomas in other tissues and that its expression in normal tissues is nearly restricted to germ cells and placental trophoblasts. These results indicate that dbpC/contrin would be a potentially novel cancer/testis antigen