93 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
Geometry of Particle Physics
We construct a large class of new quiver gauge theories from branes at singularities by orientifolding and Higgsing old examples. The new models include the MSSM, decoupled from gravity, as well as some classic models of dynamical SUSY breaking. We also discuss topological criteria for unification
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
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