53 research outputs found
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
- …