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

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

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

SO/Sp Monopoles and Branes with Orientifold 3 Plane

We study BPS monopoles in 4 dimensional N=4 SO(N) and $Sp(N)$ super Yang-Mills theories realized as the low energy effective theory of $N$ (physical and its mirror) parallel D3 branes and an {\it Orientifold 3 plane} with D1 branes stretched between them in type IIB string theory. Monopoles on D3 branes give the natural understanding by embedding in SU(N) through the constraints on both the asymptotic Higgs field (corresponding to the horizontal positions of D3 branes) and the magnetic charges (corresponding to the number of D1 branes) imposed by the O3 plane. The compatibility conditions of Nahm data for monopoles for these groups can be interpreted very naturally through the D1 branes in the presence of O3 plane.Comment: 18 pages, Latex with RevTex, 1 table, 4 figures, v2: Clarified the introduction and improved on the supersymmetric theory on D1 branes in page 7 and 8 and this final version to appear in Phys.Rev.

Gauge Theories with Tensors from Branes and Orientifolds

We present brane constructions in Type IIA string theory for N=1 supersymmetric SO and Sp gauge theories with tensor representations using an orientifold 6-plane. One limit of these set-ups corresponds to N=2 theories previously constructed by Landsteiner and Lopez, while a different limit yields N=1 SO or Sp theories with a massless tensor and no superpotential. For the Sp-type orientifold projection comparison with the field theory moduli space leads us to postulate two new rules governing the stability of configurations of D-branes intersecting the orientifold. Lifting one of our configurations to M-theory by finding the corresponding curves, we re-derive the N=1 dualities for SO and Sp groups using semi-infinite D4 branes.Comment: Discussion on duality in U(N) with a symmetric or antisymmetric flavor added to Section 4. Typos fixe

Froggatt-Nielsen models from E8 in F-theory GUTs

This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks: R-parity must be imposed by hand and there is a doublet-triplet splitting problem.Comment: 42 pages; v2:journal version; v3:corrected typo in neutrino masse

Orbifolds, Penrose Limits and Supersymmetry Enhancement

We consider supersymmetric PP-wave limits for different N=1 orbifold geometries of the five sphere S^5 and the five dimensional Einstein manifold T^{1,1}. As there are several interesting ways to take the Penrose limits, the PP-wave geometry can be either maximal supersymmetric N=4 or half-maximal supersymmetric N=2. We discuss in detail the cases AdS_5 x S^5/Z_3, AdS_5 x S^5/(Z_m x Z_n) and AdS_5 x T^{1,1}/(\Z_m \times \Z_n) and we identify the gauge invariant operators which correspond to stringy excitations for the different limits.Comment: 22 pages, Latex,v2:additional comments in section 2,references update

Pseudomoduli Dark Matter and Quiver Gauge Theories

We investigate supersymmetric models for dark matter which is represented by pseudomoduli in weakly coupled hidden sectors. We propose a scheme to add a dark matter sector to quiver gauge theories with metastable supersymmetry breaking. We discuss the embedding of such scheme in string theory and we describe the dark matter sector in terms of D7 flavour branes. We explore the phenomenology in various regions of the parameters.Comment: 24 pages, 12 figures, JHEP3.cl