2,551 research outputs found

### de Sitter Vacua in Type IIB String Theory: Classical Solutions and Quantum Corrections

We revisit the classical theory of ten-dimensional two-derivative gravity coupled to fluxes, scalar fields, D-branes, anti D-branes and Orientifold-planes. We show that such set-ups do not give rise to a four-dimensional positive curvature spacetime with the isometries of de Sitter spacetime. We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled. Our analysis relies on the derivation of the de Sitter condition from an explicit background solution by going beyond the supergravity limit of type IIB theory. As such this also tells us how the background supersymmetry should be broken and under what conditions D-term uplifting can be realized with non self-dual fluxes

### Flavor Structure in F-theory Compactifications

F-theory is one of frameworks in string theory where supersymmetric grand
unification is accommodated, and all the Yukawa couplings and Majorana masses
of right-handed neutrinos are generated. Yukawa couplings of charged fermions
are generated at codimension-3 singularities, and a contribution from a given
singularity point is known to be approximately rank 1. Thus, the approximate
rank of Yukawa matrices in low-energy effective theory of generic F-theory
compactifications are minimum of either the number of generations N_gen = 3 or
the number of singularity points of certain types. If there is a geometry with
only one E_6 type point and one D_6 type point over the entire 7-brane for
SU(5) gauge fields, F-theory compactified on such a geometry would reproduce
approximately rank-1 Yukawa matrices in the real world. We found, however, that
there is no such geometry. Thus, it is a problem how to generate hierarchical
Yukawa eigenvalues in F-theory compactifications. A solution in the literature
so far is to take an appropriate factorization limit. In this article, we
propose an alternative solution to the hierarchical structure problem (which
requires to tune some parameters) by studying how zero mode wavefunctions
depend on complex structure moduli. In this solution, the N_gen x N_gen CKM
matrix is predicted to have only N_gen entries of order unity without an extra
tuning of parameters, and the lepton flavor anarchy is predicted for the lepton
mixing matrix. We also obtained a precise description of zero mode
wavefunctions near the E_6 type singularity points, where the up-type Yukawa
couplings are generated.Comment: 148 page

### Phase Structure of a Brane/Anti-Brane System at Large N

We further analyze a class of recently studied metastable string vacua
obtained by wrapping D5-branes and anti-D5-branes over rigid homologous S^2's
of a non-compact Calabi-Yau threefold. The large N dual description is
characterized by a potential for the glueball fields which is determined by an
auxiliary matrix model. The higher order corrections to this potential produce
a suprisingly rich phase structure. In particular, at sufficiently large 't
Hooft coupling the metastable vacua present at weak coupling cease to exist.
This instability can already be seen by an open string two loop contribution to
the glueball potential. The glueball potential also lifts some of the
degeneracy in the vacua characterized by the phases of the glueball fields.
This generates an exactly computable non-vanishing axion potential at large N.Comment: v3: 55 pages, 11 figures, typos correcte

### Blow up for the wave equation with a fractional damping

Abstract. We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time

### Domain Walls in MQCD and Monge-Ampere Equation

We study Witten's proposal that a domain wall exists in M-theory fivebrane
version of QCD (MQCD) and that it can be represented as a supersymmetric
three-cycle in G_2 holonomy manifold. It is shown that equations defining the
U(1) invariant domain wall for SU(2) group can be reduced to the Monge-Ampere
equation. A proof of an algebraic formula of Kaplunovsky, Sonnenschein and
Yankielowicz is presented. The formal solution of equations for domain wall is
constructed.Comment: Latex, 18 pages, section 4.2 modified, typos correcte

### Geometric Transition versus Cascading Solution

We study Vafa's geometric transition and Klebanov - Strassler solution from
various points of view in M-theory. In terms of brane configurations, we show
the detailed equivalences between the two models. In some limits, both models
have an alternative realization as fourfolds in M-theory with appropriate
G-fluxes turned on. We discuss some aspects of the fourfolds including how to
see the transition and a possible extension to the non-supersymmetric case.Comment: 34 pages, LaTex, 2 figures; v2: Some comments added and references
updated. Final version to appear in JHE

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