1,318 research outputs found
The Seiberg-Witten prepotential and the Euler class of the reduced moduli space of instantons
The n-instanton contribution to the Seiberg-Witten prepotential of N=2
supersymmetric d=4 Yang Mills theory is represented as the integral of the
exponential of an equivariantly exact form. Integrating out an overall scale
and a U(1) angle the integral is rewritten as (4n-3) fold product of a closed
two form. This two form is, formally, a representative of the Euler class of
the Instanton moduli space viewed as a principal U(1) bundle, because its
pullback under bundel projection is the exterior derivative of an angular
one-form.Comment: LaTex, 15 page
Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
We show how the Dijkgraaf-Vafa matrix model proposal can be extended to
describe five-dimensional gauge theories compactified on a circle to four
dimensions. This involves solving a certain quantum mechanical matrix model. We
do this for the lift of the N=1* theory to five dimensions. We show that the
resulting expression for the superpotential in the confining vacuum is
identical with the elliptic superpotential approach based on Nekrasov's
five-dimensional generalization of Seiberg-Witten theory involving the
relativistic elliptic Calogero-Moser, or Ruijsenaars-Schneider, integrable
system.Comment: 11 pages, 2 figures, JHEP3.cls, important references adde
Exact Superpotentials from Matrix Models
Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a
large class of N=1 SUSY gauge theories can be extracted from the planar limit
of a certain holomorphic matrix integral. We test their proposal against
existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory
involving an arbitrary polynomial superpotential for one of the three adjoint
chiral superfields. Specifically, we compare the DV prediction for these models
with earlier results based on the connection between SUSY gauge theories and
integrable systems. We find complete agreement between the two approaches. In
particular we show how the DV proposal allows the extraction of the exact
eigenvalues of the adjoint scalar in the confining vacuum and hence computes
all related condensates of the finite-N gauge theory. We extend these results
to include Leigh-Strassler deformations of the N=4 theory.Comment: 28 pages, 1 figure, latex with JHEP.cls, replaced with typos
corrected and one clarifying commen
On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
We determine the exact vacuum structure of a marginal deformation of N=4 SUSY
Yang-Mills with gauge group U(N). The Coulomb branch of the theory consists of
several sub-branches which are governed by complex curves of the form
Sigma_{n_{1}} U Sigma_{n_{2}} U Sigma_{n_{3}} of genus N=n_{1}+n_{2}+n_{3}.
Each sub-branch intersects with a family of Higgs and Confining branches
permuted by SL(2,Z) transformations. We determine the curve by solving a
related matrix model in the planar limit according to the prescription of
Dijkgraaf and Vafa, and also by explicit instanton calculations using a form of
localization on the instanton moduli space. We find that Sigma_{n} coincides
with the spectral curve of the n-body Ruijsenaars-Schneider system. Our results
imply that the theory on each sub-branch is holomorphically equivalent to
certain five-dimensional gauge theory with eight supercharges. This equivalence
also implies the existence of novel confining branches in five dimensions.Comment: LaTeX file. 48 page
Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
The spectra of a particular class of PT symmetric eigenvalue problems has
previously been studied, and found to have an extremely rich structure. In this
paper we present an explanation for these spectral properties in terms of
quantisation conditions obtained from the complex WKB method. In particular, we
consider the relation of the quantisation conditions to the reality and
positivity properties of the eigenvalues. The methods are also used to examine
further the pattern of eigenvalue degeneracies observed by Dorey et al. in
[1,2].Comment: 22 pages, 13 figures. Added references, minor revision
Another Leigh-Strassler deformation through the Matrix model
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to
obtain the effective superpotential for a certain deformation of N=4 SYM
discovered by Leigh and Strassler. An exact solution to the matrix model
Lagrangian is found and is expressed in terms of elliptic functions.Comment: 15 pages,2 figure
Screen Printed PZT Thick Films Using Composite Film Technology
A spin coating composite sol gel technique for producing lead zirconate titanate (PZT) thick films has been modified for use with screen printing techniques. The resulting screen printing technique can be used to produce 10 ?m thick films in a single print. The resultant films are porous but the density can be increased through the use of repeated sol infiltration/pyrolysis treatments to yield a high density film. When fired at 710°C the composite screen printed films have dielectric and piezoelectric properties comparable to, or exceeding, those of films produced using a 'conventional' powder/glass frit/oil ink and fired at 890°C
New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
Using the result of a matrix model computation of the exact glueball
superpotential, we investigate the relevant mass perturbations of the
Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory.
We recall a conjecture for the elliptic superpotential that describes the
theory compactified on a circle and identify this superpotential as one of the
Hamiltonians of the elliptic Ruijsenaars-Schneider integrable system. In the
limit that the Leigh-Strassler deformation is turned off, the integrable system
reduces to the elliptic Calogero-Moser system which describes the N=1^* theory.
Based on these results, we identify the Coulomb branch of the partially
mass-deformed Leigh-Strassler theory as the spectral curve of the
Ruijsenaars-Schneider system. We also show how the Leigh-Strassler deformation
may be obtained by suitably modifying Witten's M theory brane construction of
N=2 theories.Comment: 13 pages, JHEP, amstex, changed JHEP to JHEP
Affine Toda field theory on a half line
The question of the integrability of real-coupling affine toda field theory
on a half-line is addressed. It is found, by examining low-spin conserved
charges, that the boundary conditions preserving integrability are strongly
constrained. In particular, for the series of models there can be
no free parameters introduced by the boundary condition; indeed the only
remaining freedom (apart from choosing the simple condition ), resides in a choice of signs. For a special case of the boundary
condition, it is argued that the classical boundary bound state spectrum is
closely related to a consistent set of reflection factors in the quantum field
theory.Comment: 16 pages, TEX (harvmac), DTP-94/7, YITP/U-94-1
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