1,185 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
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
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
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
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
Wall Crossing and Instantons in Compactified Gauge Theory
We calculate the leading weak-coupling instanton contribution to the
moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group
SU(2) compactified on R^3 x S^1. The results are in precise agreement with the
semiclassical expansion of the exact metric recently conjectured by Gaiotto,
Moore and Neitzke based on considerations related to wall-crossing in the
corresponding four-dimensional theory.Comment: 24 pages, no figure
The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory
The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry,
broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is
determined exactly by compactifying the theory on a circle of finite radius.
The exact low-energy superpotential is constructed by identifying it as a
linear combination of the Hamiltonians of a certain symplectic reduction of the
spin generalized elliptic Calogero-Moser integrable system. It is shown that
the theory has four confining, two Higgs and two massless Coulomb vacua which
agrees with a simple analysis of the tree-level superpotential of the
four-dimensional theory. In each vacuum, we calculate all the condensates of
the adjoint-valued scalars.Comment: 12 pages, JHEP.cl
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
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