5,978 research outputs found
Axion Inflation in F-theory
We study the dynamics of axion-like fields in F-theory and suggest that they
can serve as inflatons in models of natural inflation. The axions arise from
harmonic three-forms on the F-theory compactification space and parameterize a
complex torus that varies over the geometric moduli space. In particular, this
implies that the axion decay constants depend on the complex structure moduli
that can be fixed by background fluxes. This might allow tuning them to be
super-Planckian in a controlled way and allow for interesting single field
inflationary models. We argue that this requires a localization of the
three-forms near regions of strong string coupling, analogously to the
reasoning that GUT physics requires the use of F-theory. These models can admit
a tensor to scalar ratio r>0.1.Comment: 9 pages, 1 figure; v2: added clarifying remarks and reference
The N=1 effective action of F-theory compactifications
The four-dimensional N=1 effective action of F-theory compactified on a
Calabi-Yau fourfold is studied by lifting a three-dimensional M-theory
compactification. The lift is performed by using T-duality realized via a
Legendre transform on the level of the effective action, and the application of
vector-scalar duality in three dimensions. The leading order Kahler potential
and gauge-kinetic coupling functions are determined. In these compactifications
two sources of gauge theories are present. Space-time filling non-Abelian
seven-branes arise at the singularities of the elliptic fibration of the
fourfold. Their couplings are included by resolving the singular fourfold.
Generically a U(1)^r gauge theory arises from the R-R bulk sector if the base
of the elliptically fibered Calabi-Yau fourfold supports 2r harmonic
three-forms. The gauge coupling functions depend holomorphically on the complex
structure moduli of the fourfold, comprising closed and open string degrees of
freedom. The four-dimensional electro-magnetic duality is studied in the
three-dimensional effective theory obtained after M-theory compactification. A
discussion of matter couplings transforming in the adjoint of the seven-brane
gauge group is included.Comment: 59 pages, v2: references added, typos correcte
On Mirror Symmetry for Calabi-Yau Fourfolds with Three-Form Cohomology
We study the action of mirror symmetry on two-dimensional N=(2,2) effective
theories obtained by compactifying Type IIA string theory on Calabi-Yau
fourfolds. Our focus is on fourfold geometries with non-trivial three-form
cohomology. The couplings of the massless zero-modes arising by expanding in
these forms depend both on the complex structure deformations and the Kahler
structure deformations of the Calabi-Yau fourfold. We argue that two
holomorphic functions of the deformation moduli capture this information. These
are exchanged under mirror symmetry, which allows us to derive them at the
large complex structure and large volume point. We discuss the application of
the resulting explicit expression to F-theory compactifications and their weak
string coupling limit. In the latter orientifold settings we demonstrate
compatibility with mirror symmetry of Calabi-Yau threefolds at large complex
structure. As a byproduct we find an interesting relation of no-scale like
conditions on Kahler potentials to the existence of chiral and twisted-chiral
descriptions in two dimensions.Comment: 36 page
Self-Dual Tensors and Partial Supersymmetry Breaking in Five Dimensions
We study spontaneous supersymmetry breaking of five-dimensional supergravity
theories from sixteen to eight supercharges in Minkowski vacua. This N=4 to N=2
breaking is induced by Abelian gaugings that require the introduction of
self-dual tensor fields accompanying the vectors in the gravity multiplet and
vector multiplets. These tensor fields have first-order kinetic terms and can
become massive by a Stueckelberg-like mechanism. We identify the general class
of N=2 vacua and show how the N=4 spectrum splits into massless and massive N=2
multiplets. In particular, we find a massive gravitino multiplet, containing
two complex massive tensors, and a number of massive tensor multiplets and
hypermultiplets. We determine the resulting N=2 effective action for the
massless multiplets obtained by integrating out massive fields. We show that
the metric and Chern-Simons terms of the vectors are corrected at one-loop by
massive tensors as well as spin-1/2 and spin-3/2 fermions. These contributions
are independent of the supersymmetry-breaking scale and thus have to be
included at arbitrarily low energies.Comment: 33 page
The N=1 effective actions of D-branes in Type IIA and IIB orientifolds
We discuss the four-dimensional N=1 effective actions of single space-time
filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold
compactifications. The effective actions depend on an infinite number of normal
deformations and gauge connection modes. For D6-branes the N=1 Kaehler
potential, the gauge-coupling function, the superpotential and the D-terms are
determined as functions of these fields. They can be expressed as integrals
over chains which end on the D-brane cycle and a reference cycle. The infinite
deformation space will reduce to a finite-dimensional moduli space of special
Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions.
We show that the Type IIA moduli space geometry is captured by three real
functionals encoding the deformations of special Lagrangian submanifolds,
holomorphic three-forms and Kaehler two-forms of Calabi-Yau manifolds. These
elegantly combine in the N=1 Kaehler potential, which reduces after applying
mirror symmetry to the results previously determined for space-time filling
D3-, D5- and D7-branes. We also propose general chain integral expressions for
the Kaehler potentials of Type IIB D-branes.Comment: 61 pages, v2: typos corrected and refs adde
Chiral anomalies on a circle and their cancellation in F-theory
We study in detail how four-dimensional local anomalies manifest themselves
when the theory is compactified on a circle. By integrating out the
Kaluza-Klein modes in a way that preserves the four-dimensional symmetries in
the UV, we show that the three-dimensional theory contains field-dependent
Chern-Simons terms that appear at one-loop. These vanish if and only if the
four-dimensional anomaly is canceled, so the anomaly is not lost upon
compactification. We extend this analysis to situations where anomalies are
canceled through a Green-Schwarz mechanism. We then use these results to show
automatic cancellation of local anomalies in F-theory compactifications that
can be obtained as a limit of M-theory on a smooth Calabi-Yau fourfold with
background flux.Comment: 39 pages, 3 figures. v2: references added and typos correcte
Complete Intersection Fibers in F-Theory
Global F-theory compactifications whose fibers are realized as complete
intersections form a richer set of models than just hypersurfaces. The detailed
study of the physics associated with such geometries depends crucially on being
able to put the elliptic fiber into Weierstrass form. While such a
transformation is always guaranteed to exist, its explicit form is only known
in a few special cases. We present a general algorithm for computing the
Weierstrass form of elliptic curves defined as complete intersections of
different codimensions and use it to solve all cases of complete intersections
of two equations in an ambient toric variety. Using this result, we determine
the toric Mordell-Weil groups of all 3134 nef partitions obtained from the 4319
three-dimensional reflexive polytopes and find new groups that do not exist for
toric hypersurfaces. As an application, we construct several models that cannot
be realized as toric hypersurfaces, such as the first toric SU(5) GUT model in
the literature with distinctly charged 10 representations and an F-theory model
with discrete gauge group Z_4 whose dual fiber has a Mordell-Weil group with
Z_4 torsion.Comment: 41 pages, 4 figures and 18 tables; added references in v
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