202 research outputs found
Solutions of the Generic Non-Compact Weyl Equation
In this paper, solutions of the generic non-compact Weyl equation are
obtained. In particular, by identifying a suitable similarity transformation
and introducing a non-trivial change of variables we are able to implement
azimuthal dependence on the solutions of the diagonal non-compact Weyl
equation. We also discuss some open questions related to the construction of
infinite BPS monopole configurations.Comment: 12 pages, Latex. Few extra comments and a reference adde
Spectral data for simply periodic solutions of the sinh-Gordon equation
This note summarizes results that were obtained by the author in his habilitation thesis concerning the development of a spectral theory for simply periodic, 2-dimensional, complex-valued solutions u of the sinh-Gordon equation. Spectral data for such solutions are defined for periodic Cauchy data on a line (following Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data of such Cauchy data is answered. Finally a Jacobi variety for the spectral curve is constructed, and this is used to study the asymptotic behavior of the spectral data corresponding to actual simply periodic solutions of the sinh-Gordon equation on strips of positive height
Some comments on spacelike minimal surfaces with null polygonal boundaries in
We discuss some geometrical issues related to spacelike minimal surfaces in
with null polygonal boundaries at conformal infinity. In particular for
, two holomorphic input functions for the Pohlmeyer reduced system are
identified. This system contains two coupled differential equations for two
functions and , related to curvature and
torsion of the surface. Furthermore, we conjecture that, for a polynomial
choice of the two holomorphic functions, the relative positions of their zeros
encode the conformal invariant data of the boundary null -gon.Comment: 13 pages, a note and references added, version to appear in JHE
The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality
We study the construction of generalized Kahler manifolds, described purely
in terms of N=(2,2) semichiral superfields, by a quotient using the semichiral
vector multiplet. Despite the presence of a b-field in these models, we show
that the quotient of a hyperkahler manifold is hyperkahler, as in the usual
hyperkahler quotient. Thus, quotient manifolds with torsion cannot be
constructed by this method. Nonetheless, this method does give a new
description of hyperkahler manifolds in terms of two-dimensional N=(2,2) gauged
non-linear sigma models involving semichiral superfields and the semichiral
vector multiplet. We give two examples: Eguchi-Hanson and Taub-NUT. By
T-duality, this gives new gauged linear sigma models describing the T-dual of
Eguchi-Hanson and NS5-branes. We also clarify some aspects of T-duality
relating these models to N=(4,4) models for chiral/twisted-chiral fields and
comment briefly on more general quotients that can give rise to torsion and
give an example.Comment: 31 page
Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures
We study the basic properties of Higgs sheaves over compact K\"ahler
manifolds and we establish some results concerning the notion of semistability;
in particular, we show that any extension of semistable Higgs sheaves with
equal slopes is semistable. Then, we use the flattening theorem to construct a
regularization of any torsion-free Higgs sheaf and we show that it is in fact a
Higgs bundle. Using this, we prove that any Hermitian metric on a
regularization of a torsion-free Higgs sheaf induces an admissible structure on
the Higgs sheaf. Finally, using admissible structures we proved some properties
of semistable Higgs sheaves.Comment: 18 pages; some typos correcte
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
Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets
We discuss the conditions for extra supersymmetry of the N=(2,2)
supersymmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in
arXiv:0808.1535 [hep-th]. We find (4,4) supersymmetry for the semichiral vector
multiplet but not for the Large Vector Multiplet.Comment: 15 page
General Argyres-Douglas Theory
We construct a large class of Argyres-Douglas type theories by compactifying
six dimensional (2,0) A_N theory on a Riemann surface with irregular
singularities. We give a complete classification for the choices of Riemann
surface and the singularities. The Seiberg-Witten curve and scaling dimensions
of the operator spectrum are worked out. Three dimensional mirror theory and
the central charges a and c are also calculated for some subsets, etc. Our
results greatly enlarge the landscape of N=2 superconformal field theory and in
fact also include previous theories constructed using regular singularity on
the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte
Construction et classification de certaines solutions algébriques des systÚmes de Garnier
22 pagesInternational audienceIn this paper, we classify all (complete) non elementary algebraic solutions of Garnier systems that can be constructed by Kitaev's method: they are deduced from isomonodromic deformations defined by pulling back a given fuchsian equation E by a family of ramified covers. We first introduce orbifold structures associated to a fuchsian equation. This allow to get a refined version of Riemann-Hurwitz formula and then to promtly deduce that E is hypergeometric. Then, we can bound exponents and degree of the pull-back maps and further list all possible ramification cases. This generalizes a result due to C. Doran for the Painleve VI case. We explicitely construct one of these solutions
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.
- âŠ