1,508 research outputs found
One-instanton test of the exact prepotential for N=2 SQCD coupled to a symmetric tensor hypermultiplet
Using the ADHM instanton calculus, we evaluate the one-instanton contribution
to the low-energy effective prepotential of N=2 supersymmetric SU(N) Yang-Mills
theory with N_F flavors of hypermultiplets in the fundamental representation
and a hypermultiplet in the symmetric rank two tensor representation. For
N_F<N-2, when the theory is asymptotically free, our result is compared with
the exact solution that was obtained using M-theory and we find complete
agreement.Comment: 11 pages, LaTeX, no figure
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
N=1* vacua, Fuzzy Spheres and Integrable Systems
We calculate the exact eigenvalues of the adjoint scalar fields in the
massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a
field theory prediction for the distribution of D3 brane charge in the AdS
dual. We verify the proposal of Polchinski and Strassler that the D3-brane's
lie on a fuzzy sphere in the supergravity limit and determine the corrections
to this distribution due to worldsheet and quantum effects. The calculation
also provides several new results concerning the equilibrium configurations of
the N-body Calogero-Moser Hamiltonian.Comment: 20 page
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
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
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
On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter
We present a qualitative model of the Coulomb branch of the moduli space of
low-energy effective N=2 SQCD with gauge group SU(3) and up to five flavours of
massive matter. Overall, away from double cores, we find a situation broadly
similar to the case with no matter, but with additional complexity due to the
proliferation of extra BPS states. We also include a revised version of the
pure SU(3) model which can accommodate just the orthodox weak coupling
spectrum.Comment: 32 pages, 25 figures, uses JHEP.cls, added references, deleted joke
An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories
We study relevant deformations of the N=2 superconformal theory on the
world-volume of N D3 branes at an A_{k-1} singularity. In particular, we
determine the vacuum structure of the mass-deformed theory with N=1
supersymmetry and show how the different vacua are permuted by an extended
duality symmetry. We then obtain exact, modular covariant formulae (for all k,
N and arbitrary gauge couplings) for the holomorphic observables in the massive
vacua in two different ways: by lifting to M-theory, and by compactification to
three dimensions and subsequent use of mirror symmetry. In the latter case, we
find an exact superpotential for the model which coincides with a certain
combination of the quadratic Hamiltonians of the spin generalization of the
elliptic Calogero-Moser integrable system.Comment: 55 pages, 5 figures, latex with JHEP.cl
S-duality of the Leigh-Strassler Deformation via Matrix Models
We investigate an exactly marginal N=1 supersymmetric deformation of SU(N)
N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use
a matrix model to compute the exact superpotential for a further massive
deformation of the U(N) Leigh-Strassler theory. We then show how the exact
superpotential and eigenvalue spectrum for the SU(N) theory follows by a
process of integrating-in. We find that different vacua are related by an
action of the SL(2,Z) modular group on the bare couplings of the theory
extending the action of electric-magnetic duality away from the N=4 theory. We
perform non-trivial tests of the matrix model results against semiclassical
field theory analysis. We also show that there are interesting points in
parameter space where condensates can diverge and vacua disappear. Based on the
matrix model results, we propose an exact elliptic superpotential to describe
the theory compactified on a circle of finite radius.Comment: 33 pages, 2 figures, uses JHEP.cls; minus sign typo corrected and 1
reference added, submitted to JHE
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
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