3,803 research outputs found
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
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
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
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
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