3,766 research outputs found
Appell F1 and Conformal Mapping
This is the last of a trilogy of papers on triangle centers. A fairly obscure
"conformal center of gravity" is computed for the class of all isosceles
triangles. This calculation appears to be new. A byproduct is the logarithmic
capacity or transfinite diameter of such, yielding results consistent with
Haegi (1951).Comment: 12 pages, 3 figure
The Collective Field Theory of a Singular Supersymmetric Matrix Model
The supersymmetric collective field theory with the potential is studied, motivated by the matrix model proposed by Jevicki
and Yoneya to describe two dimensional string theory in a black hole
background. Consistency with supersymmetry enforces a two band solution. A
supersymmetric classical configuration is found, and interpreted in terms of
the density of zeros of certain Laguerre polynomials. The spectrum of the model
is then studied and is seen to correspond to a massless scalar and a majorana
fermion. The space eigenfunctions are constructed and expressed in terms of
Chebyshev polynomials. Higher order interactions are also discussed.Comment: Revtex 8 pages, Submitted to Phys. Rev. D. References and preprint
numbers have been adde
Operator product expansion of higher rank Wilson loops from D-branes and matrix models
In this paper we study correlation functions of circular Wilson loops in
higher dimensional representations with chiral primary operators of N=4 super
Yang-Mills theory. This is done using the recently established relation between
higher rank Wilson loops in gauge theory and D-branes with electric fluxes in
supergravity. We verify our results with a matrix model computation, finding
perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde
Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential
The bound state energy eigenvalues and the corresponding eigenfunctions of
the generalized Woods Saxon potential are obtained in terms of the Jacobi
polynomials. Nikiforov Uvarov method is used in the calculations. It is shown
that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review
Bulk Universality and Related Properties of Hermitian Matrix Models
We give a new proof of universality properties in the bulk of spectrum of the
hermitian matrix models, assuming that the potential that determines the model
is globally and locally function (see Theorem \ref{t:U.t1}).
The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal
polynomial techniques but does not use asymptotics of orthogonal polynomials.
Rather, we obtain the -kernel as a unique solution of a certain non-linear
integro-differential equation that follows from the determinant formulas for
the correlation functions of the model. We also give a simplified and
strengthened version of paper \cite{BPS:95} on the existence and properties of
the limiting Normalized Counting Measure of eigenvalues. We use these results
in the proof of universality and we believe that they are of independent
interest
Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schr\"odinger Operators
We announce three results in the theory of Jacobi matrices and Schr\"odinger
operators. First, we give necessary and sufficient conditions for a measure to
be the spectral measure of a Schr\"odinger operator -\f{d^2}{dx^2} +V(x) on
with and boundary condition.
Second, we give necessary and sufficient conditions on the Jacobi parameters
for the associated orthogonal polynomials to have Szeg\H{o} asymptotics.
Finally, we provide necessary and sufficient conditions on a measure to be the
spectral measure of a Jacobi matrix with exponential decay at a given rate.Comment: 10 page
Holography, Pade Approximants and Deconstruction
We investigate the relation between holographic calculations in 5D and the
Migdal approach to correlation functions in large N theories. The latter
employs Pade approximation to extrapolate short distance correlation functions
to large distances. We make the Migdal/5D relation more precise by quantifying
the correspondence between Pade approximation and the background and boundary
conditions in 5D. We also establish a connection between the Migdal approach
and the models of deconstructed dimensions.Comment: 28 page
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