1,254 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
G_4 flux, chiral matter and singularity resolution in F-theory compactifications
We construct a set of chirality inducing G_4-fluxes in global F-theory
compactifications on Calabi-Yau four-folds. Special emphasis is put on models
with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model
building, which are described in terms of a U(1)-restricted Tate model. In this
type of constructions, the G_4-flux arises in a manner completely analogous to
the U(1)_X gauge potential. We describe in detail the resolution by blow-up of
the various singularities responsible for the U(1)_X factor and the standard
SU(5) gauge group and match the result with techniques applied in the context
of toric geometry. This provides an explicit identification of the structure of
the resolved fibre over the matter curves and over the enhancement points
relevant for Yukawa couplings. The U(1)_X flux induces a chiral matter
spectrum. We compute the chiral index both of SU(5) charged matter and of SU(5)
singlets charged only under U(1)_X localised on curves which are not contained
in the SU(5) locus. We furthermore discuss global consistency conditions such
as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation.
The U(1)_X gauge flux is a global extension of a class of split spectral cover
bundles. It constitutes an essential ingredient in the construction of globally
defined F-theory compactifications with chiral matter. We exemplify this in a
three-generation SU(5) x U(1)_X model whose flux satisfies all of the above
global consistency conditions. We also extend our results to chiral fluxes in
models without U(1) restriction.Comment: 53 pages, 2 figures; v2: details on Freed-Witten quantisation
condition included, typos correcte
G-flux and Spectral Divisors
We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold
compactifications of F-theory, which in the local limit allow a spectral cover
description. The main tool of construction is the so-called spectral divisor in
the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs
bundle spectral cover. We exemplify the workings of this in the case of an E_6
singularity by constructing the resolved geometry, the spectral divisor and in
the local limit, the spectral cover. The G-flux constructed with the spectral
divisor is shown to be equivalent to the direct construction from suitably
quantized linear combinations of holomorphic surfaces in the resolved geometry,
and in the local limit reduces to the spectral cover flux.Comment: 30 page
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
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
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