74 research outputs found
Statistics of Flux Vacua for Particle Physics
Supersymmetric flux compactification of F-theory in the geometric phase
yields numerous vacua, and provides an ensemble of low-energy effective
theories with different symmetry, matter multiplicity and Lagrangian
parameters. Theoretical tools have already been developed so that we can study
how the statistics of flux vacua depend on the choice of symmetry and some of
Lagrangian parameters. In this article, we estimate the fraction of i) vacua
that have a U(1) symmetry for spontaneous R-parity violation, and ii) those
that realise ideas which achieve hierarchical eigenvalues of the Yukawa
matrices. We also learn a lesson that the number of flux vacua is reduced very
much when the unbroken symmetry is obtained from a non-trivial
Mordell--Weil group, while it is not when is in SU(5) unification. It
also turns out that vacua with an approximate U(1) symmetry forms a locus of
accumulation points of the flux vacua distribution.Comment: 51 page
Supergravity Analysis of Hybrid Inflation Model from D3--D7 System
The slow-roll inflation is a beautiful paradigm, yet the inflaton potential
can hardly be sufficiently flat when unknown gravitational effects are taken
into account. However, the hybrid inflation models constructed in D = 4 N = 1
supergravity can be consistent with N = 2 supersymmetry, and can be naturally
embedded into string theory. This article discusses the gravitational effects
carefully in the string model, using D = 4 supergravity description. We adopt
the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2
orientifold for definiteness. It turns out that the slow-roll parameter can be
sufficiently small despite the non-minimal Kahler potential of the model. The
conditions for this to happen are clarified in terms of string vacua. We also
find that the geometry obtained by blowing up singularity, which is necessary
for the positive vacuum energy, is stabilized by introducing certain 3-form
fluxes.Comment: 21 pages; v3. a typo corrected, and some changes made in sections 4.1
and 4.2, accordingl
Pure Natural Inflation
We point out that a simple inflationary model in which the axionic inflaton
couples to a pure Yang-Mills theory may give the scalar spectral index (n_s)
and tensor-to-scalar ratio (r) in complete agreement with the current
observational data.Comment: 4 pages, 3 figures, published versio
String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
It is known that the L-function of an elliptic curve defined over Q is given
by the Mellin transform of a modular form of weight 2. Does that modular form
have anything to do with string theory? In this article, we address a question
along this line for elliptic curves that have complex multiplication defined
over number fields. So long as we use diagonal rational N=(2,2) superconformal
field theories for the string-theory realizations of the elliptic curves, the
weight-2 modular form turns out to be the Boltzmann-weighted
(q^{L_0-c/24}-weighted) sum of U(1) charges with F e^{ \pi i F} insertion
computed in the Ramond sector.Comment: 48 pages; minor corrections and improvements in v
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