Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's

We use the resolution procedure of Esole and Yau arXiv:1107.0733 to study Yukawa couplings, G-flux, and the emergence of spectral covers from elliptically fibered Calabi-Yau's with a surface of A_4 singularities. We provide a global description of the Esole-Yau resolution and use it to explicitly compute Chern classes of the resolved 4-fold, proving the conjecture of arXiv:0908.1784 for the Euler character in the process. We comment on the physical implications of the surprising singular fibers in codimension 2 and 3 in arXiv:1107.0733 and emphasize a group theoretic interpretation based on the A_4 weight lattice. We then construct explicit G-fluxes by brute force in one of the 6 birationally equivalent Esole-Yau resolutions, quantize them explicitly using our result for the second Chern class, and compute the spectrum and flux-induced 3-brane charges, finding agreement with results and conjectures of local models in all cases. Finally, we provide a precise description of the spectral divisor formalism in this setting and sharpen the procedure described in arXiv:1107.1718 in order to explicitly demonstrate how the Higgs bundle spectral cover of the local model emerges from the resolved Calabi-Yau geometry. Along the way, we demonstrate explicitly how the quantization rules for fluxes in the local and global models are related.Comment: 68 pages (41 pages + 4 appendices

Global Gluing and G-flux

Local models that capture the 7-brane physics of F-theory compactifications for supersymmetric GUTs are conveniently described in terms of an E_8 gauge theory in the presence of a Higgs bundle. Though the Higgs bundle data is usually determined by the local geometry and G-flux, additional gluing data must be specified whenever the Higgs bundle spectral cover is not smooth. In this paper, we argue that this additional information is determined by data of the M-theory 3-form that is not necessarily captured by the cohomology class of the G-flux. More specifically, we show that when the 3-form is specified in terms of a line bundle on a spectral divisor, which is a global extension of the Higgs bundle spectral cover, the gluing data of the local model is uniquely determined in a way that ensures agreement with Heterotic results whenever a Heterotic dual exists.Comment: 22 page

Gauge Mediation in F-Theory GUT Models

We study a simple framework for gauge-mediated supersymmetry-breaking in local GUT models based on F-theory 7-branes and demonstrate that a mechanism for solving both the \mu and \mu/B_{\mu} problems emerges in a natural way. In particular, a straightforward coupling of the messengers to the Higgs sector leads to a geometry which not only provides us with an approximate U(1)_{PQ} symmetry that forbids the generation of \mu at the GUT scale, it also forces the SUSY-breaking spurion field to carry a nontrivial PQ charge. This connects the breaking of SUSY to the generation of \mu so that the same scale enters both. Moreover, the messenger sector naturally realizes the D3-instanton triggered Polonyi model of arXiv:0808.1286 so this scale is exponentially suppressed relative to M_{GUT}. The effective action at low scales is in fact precisely of the form of the "sweet spot supersymmetry" scenario studied by Ibe and Kitano in arXiv:0705.3686.Comment: 34 pages, 4 figures; v4 revisions to section

Nonsupersymmetric Flux Vacua and Perturbed N=2 Systems

We geometrically engineer N=2 theories perturbed by a superpotential by adding 3-form flux with support at infinity to local Calabi-Yau geometries in type IIB. This allows us to apply the formalism of Ooguri, Ookouchi, and Park [arXiv:0704.3613] to demonstrate that, by tuning the flux at infinity, we can stabilize the dynamical complex structure moduli in a metastable, supersymmetry-breaking configuration. Moreover, we argue that this setup can arise naturally as a limit of a larger Calabi-Yau which separates into two weakly interacting regions; the flux in one region leaks into the other, where it appears to be supported at infinity and induces the desired superpotential. In our endeavor to confirm this picture in cases with many 3-cycles, we also compute the CIV-DV prepotential for arbitrary number of cuts up to fifth order in the glueball fields.Comment: 70 pages (47 pages + 4 appendices), 10 figure

F-theory GUTs with U(1) Symmetries: Generalities and Survey

We study the structure of SU(5) F-theory GUT models that engineer additional U(1) symmetries. These are highly constrained by a set of relations observed by Dudas and Palti (DP) that originate from the physics of 4D anomaly cancellation. Using the DP relations, we find a general tension between unification and the suppression of dimension 5 proton decay when one or more U(1)'s are PQ symmetries and hypercharge flux is used to break the SU(5) GUT group. We then specialize to spectral cover models, whose global completions in F- theory we know how to construct. In that setting, we provide a technical derivation of the DP relations, construct spectral covers that yield all possible solutions to them, and provide a complete survey of spectral cover models for SU(5) GUTs that exhibit two U(1) symmetries.Comment: 27 pages plus 5 appendices (70 pages total) ; v2 references adde