4,501 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
Matching Exact Results and One-Instanton Predictions in N=2 Supersymmetric SU(N) Theories
A one-instanton level test is performed for the proposed reparameterisation
scheme matching the conjectured exact low energy results and instanton
predictions for N=2 supersymmetric SU(N) gauge theories with 2N massless
fundamental matter hypermultiplets across the entire quantum moduli space. The
constants within the scheme which ensure agreement between the exact results
and the instanton predictions for general N are derived. This constitutes a
non-trivial test of the scheme, which eliminates the discrepancies arising when
the two sets of results are compared.Comment: 9 pages, LaTeX; reformatte
An Elliptic Superpotential for Softly Broken N=4 Supersymmetric Yang-Mills Theory
An exact superpotential is derived for the N=1 theories which arise as
massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The
superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to
coincide with the complexified potential of the N-body elliptic Calogero-Moser
Hamiltonian. This superpotential reproduces the vacuum structure predicted by
Donagi and Witten for the corresponding four-dimensional theory and also
transforms covariantly under the S-duality group of N=4 SYM. The analysis
yields exact formulae with interesting modular properties for the condensates
of gauge-invariant chiral operators in the four-dimensional theory.Comment: 34 pages, LaTeX. Minor corrections and an additional referenc
The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
The vacuum structure and spectra of two-dimensional gauge theories with
N=(2,2) supersymmetry are investigated. These theories admit a twisted mass
term for charged chiral matter multiplets. In the case of a U(1) gauge theory
with N chiral multiplets of equal charge, an exact description of the BPS
spectrum is obtained for all values of the twisted masses. The BPS spectrum has
two dual descriptions which apply in the Higgs and Coulomb phases of the theory
respectively. The two descriptions are related by a massive analog of mirror
symmetry: the exact mass formula which is given by a one-loop calculation in
the Coulomb phase gives predictions for an infinite series of instanton
corrections in the Higgs phase. The theory is shown to exhibit many phenomena
which are usually associated with N=2 theories in four dimensions. These
include BPS-saturated dyons which carry both topological and Noether charges,
non-trivial monodromies of the spectrum in the complex parameter space, curves
of marginal stability on which BPS states can decay and strongly coupled vacua
with massless solitons and dyons.Comment: 51 page, LaTeX, Typos correcte
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
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