26 research outputs found
Weak Coupling, Degeneration and Log Calabi-Yau Spaces
We establish a new weak coupling limit in F-theory. The new limit may be
thought of as the process in which a local model bubbles off from the rest of
the Calabi-Yau. The construction comes with a small deformation parameter
such that computations in the local model become exact as . More
generally, we advocate a modular approach where compact Calabi-Yau geometries
are obtained by gluing together local pieces (log Calabi-Yau spaces) into a
normal crossing variety and smoothing, in analogy with a similar cutting and
gluing approach to topological field theories. We further argue for a
holographic relation between F-theory on a degenerate Calabi-Yau and a dual
theory on its boundary, which fits nicely with the gluing construction.Comment: 59 pp, 2 figs, LaTe
The Sen Limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to
IIb compactifications by taking a certain limit in complex structure moduli
space, introduced by A. Sen. The limit has been characterized on the basis of
SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable
version of the Sen limit. In this picture the elliptic Calabi-Yau splits into
two pieces, a P^1-bundle and a conic bundle, and the intersection yields the
IIb space-time. We get a precise match between F-theory and perturbative type
IIb. The correspondence is holographic, in the sense that physical quantities
seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as
expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds
to summing up the D(-1)-instanton corrections to the IIb theory.Comment: 41 pp, 1 figure, LaTe
The M-Theory Three-Form and Singular Geometries
While M- and F-theory compactifications describe a much larger class of vacua
than perturbative string compactifications, they typically need singularities
to generate non-abelian gauge fields and charged matter. The physical
explanation involves M2-branes wrapped on vanishing cycles. Here we seek an
alternative explanation that could address outstanding issues such as the
description of nilpotent branches, stability walls, frozen singularities and so
forth. To this end we use a model in which the three-form is related to the
Chern-Simons form of a bundle. The model has a one-form non-abelian gauge
symmetry which normally eliminates all the degrees of freedom associated to the
bundle. However by restricting the transformations to preserve the bundle along
the vanishing cycles, we may get new degrees of freedom associated to
singularities, without appealing to wrapped M2-branes. The analysis can be
simplified by gauge-fixing the one-form symmetry using higher-dimensional
instanton equations. We explain how this mechanism leads to the natural
emergence of phenomena such as enhanced ADE gauge symmetries, nilpotent
branches, charged matter fields and their holomorphic couplings
The Sen limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the basis of SL(2, Z) monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a P -bundle and a conic bundle, and the intersection yields the IIb space-time. We get a precise match between F-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds to summing up the D(-1)-instanton corrections to the IIb theory.
Lectures on F-theory compactifications and model building
These lecture notes are devoted to formal and phenomenological aspects of
F-theory. We begin with a pedagogical introduction to the general concepts of
F-theory, covering classic topics such as the connection to Type IIB
orientifolds, the geometry of elliptic fibrations and the emergence of gauge
groups, matter and Yukawa couplings. As a suitable framework for the
construction of compact F-theory vacua we describe a special class of
Weierstrass models called Tate models, whose local properties are captured by
the spectral cover construction. Armed with this technology we proceed with a
survey of F-theory GUT models, aiming at an overview of basic conceptual and
phenomenological aspects, in particular in connection with GUT breaking via
hypercharge flux.Comment: Invited contribution to the proceedings of the CERN Winter School on
Supergravity, Strings and Gauge Theory 2010, to appear in Classical and
Quantum Gravity; 63 pages; v2: references added, typos correcte
Yukawa hierarchies at the point of in F-theory
We analyse the structure of Yukawa couplings in local SU(5) F-theory models
with enhancement. In this setting the symmetry is broken down to
SU(5) by a 7-brane configuration described by T-branes, all the Yukawa
couplings are generated in the vicinity of a point and only one family of
quarks and leptons is massive at tree-level. The other two families obtain
their masses when non-perturbative effects are taken into account, being
hierarchically lighter than the third family. However, and contrary to previous
results, we find that this hierarchy of fermion masses is not always
appropriate to reproduce measured data. We find instead that different T-brane
configurations breaking to SU(5) give rise to distinct hierarchical
patterns for the holomorphic Yukawa couplings. Only some of these patterns
allow to fit the observed fermion masses with reasonable local model parameter
values, adding further constraints to the construction of F-theory GUTs. We
consider an model where such appropriate hierarchy is realised and
compute its physical Yukawas, showing that realistic charged fermions masses
can indeed be obtained in this case.Comment: 46 pages + appendices, 5 figures. v2, added references and typos
corrected, version accepted on JHEP. v3, typos correcte
The Footprint of F-theory at the LHC
Recent work has shown that compactifications of F-theory provide a
potentially attractive phenomenological scenario. The low energy
characteristics of F-theory GUTs consist of a deformation away from a minimal
gauge mediation scenario with a high messenger scale. The soft scalar masses of
the theory are all shifted by a stringy effect which survives to low energies.
This effect can range from 0 GeV up to ~ 500 GeV. In this paper we study
potential collider signatures of F-theory GUTs, focussing in particular on ways
to distinguish this class of models from other theories with an MSSM spectrum.
To accomplish this, we have adapted the general footprint method developed
recently for distinguishing broad classes of string vacua to the specific case
of F-theory GUTs. We show that with only 5 fb^(-1) of simulated LHC data, it is
possible to distinguish many mSUGRA models and low messenger scale gauge
mediation models from F-theory GUTs. Moreover, we find that at 5 fb^(-1), the
stringy deformation away from minimal gauge mediation produces observable
consequences which can also be detected to a level of order ~ +/- 80 GeV. In
this way, it is possible to distinguish between models with a large and small
stringy deformation. At 50 fb^(-1), this improves to ~ +/- 10 GeV.Comment: 85 pages, 37 figure
Matter wave functions and Yukawa couplings in F-theory Grand Unification
We study the local structure of zero mode wave functions of chiral matter
fields in F-theory unification. We solve the differential equations for the
zero modes derived from local Higgsing in the 8-dimensional parent action of
F-theory 7-branes. The solutions are found as expansions both in powers and
derivatives of the magnetic fluxes. Yukawa couplings are given by an overlap
integral of the three wave functions involved in the interaction and can be
calculated analytically. We provide explicit expressions for these Yukawas to
second order both in the flux and derivative expansions and discuss the effect
of higher order terms. We explicitly describe the dependence of the couplings
on the U(1) charges of the relevant fields, appropriately taking into account
their normalization. A hierarchical Yukawa structure is naturally obtained. The
application of our results to the understanding of the observed hierarchies of
quarks and leptons is discussed.Comment: Latex, 51 pages, 4 figures, typos corrected, note adde
Yukawa Structure from U(1) Fluxes in F-theory Grand Unification
In F-theory GUT constructions Yukawa couplings necessarily take place at the
intersection of three matter curves. For generic geometric configurations this
gives rise to problematic Yukawa couplings unable to reproduce the observed
hierarchies. We point out that if the U(1)_{B-L}/U(1)_Y flux breaking the
SO(10)/SU(5) GUT symmetry is allowed to go through pairs of matter curves with
the same GUT representation, the quark/lepton content is redistributed in such
a way that all quark and leptons are allowed to have hierarchical Yukawas. This
reshuffling of fermions is quite unique and is particularly elegant for the
case of three generations and SO(10). Specific local F-theory models with
SO(10) or SU(5) living on a del Pezzo surface with appropriate bundles and just
the massless content of the MSSM are described. We point out that the smallness
of the 3rd generation quark mixing predicted by this scheme (together with
gauge coupling unification) could constitute a first hint of an underlying
F-theory grand unification.Comment: 31 pages, 3 figures, Latex fil