983 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
Central charges, S-duality and massive vacua of N=1* super Yang-Mills
We provide a simple derivation of the extremal values of the superpotential
in massive vacua of N=1* SYM, making use of the required modular weight for the
central charge of BPS walls interpolating between these vacua. This modular
weight descends from the action of S-duality on the N=4 superalgebra which in
turn is inherited from its classical action on the dyon spectrum. We show that
this kinematic information, combined with minimal knowledge of the weak
coupling asymptotics, is sufficient to determine the exact vacuum
superpotentials in terms of Eisenstein series.Comment: 8 pages; v2: reference added, to appear in Phys. Lett.
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
Excited state g-functions from the Truncated Conformal Space
In this paper we consider excited state g-functions, that is, overlaps
between boundary states and excited states in boundary conformal field theory.
We find a new method to calculate these overlaps numerically using a variation
of the truncated conformal space approach. We apply this method to the Lee-Yang
model for which the unique boundary perturbation is integrable and for which
the TBA system describing the boundary overlaps is known. Using the truncated
conformal space approach we obtain numerical results for the ground state and
the first three excited states which are in excellent agreement with the TBA
results. As a special case we can calculate the standard g-function which is
the overlap with the ground state and find that our new method is considerably
more accurate than the original method employed by Dorey et al.Comment: 21 pages, 6 figure
Superconformal Vortex Strings
We study the low-energy dynamics of semi-classical vortex strings living
above Argyres-Douglas superconformal field theories. The worldsheet theory of
the string is shown to be a deformation of the CP^N model which flows in the
infra-red to a superconformal minimal model. The scaling dimensions of chiral
primary operators are determined and the dimensions of the associated relevant
perturbations on the worldsheet and in the four dimensional bulk are found to
agree. The vortex string thereby provides a map between the A-series of N=2
superconformal theories in two and four dimensions.Comment: 22 pages. v2: change to introductio
Notes on Noncommutative Instantons
We study in detail the ADHM construction of U(N) instantons on noncommutative
Euclidean space-time R_{NC}^4 and noncommutative space R_{NC}^2 x R^2. We point
out that the completeness condition in the ADHM construction could be
invalidated in certain circumstances. When this happens, regular instanton
configuration may not exist even if the ADHM constraints are satisfied. Some of
the existing solutions in the literature indeed violate the completeness
condition and hence are not correct. We present alternative solutions for these
cases. In particular, we show for the first time how to construct explicitly
regular U(N) instanton solutions on R_{NC}^4 and on R_{NC}^2 x R^2. We also
give a simple general argument based on the Corrigan's identity that the
topological charge of noncommutative regular instantons is always an integer.Comment: Regular instanton solutions are now explicitly constructed also for
the case of space-space noncommutativit
NS5-Branes, T-Duality and Worldsheet Instantons
The equivalence of NS5-branes and ALF spaces under T-duality is well known.
However, a naive application of T-duality transforms the ALF space into a
smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper
we re-examine this duality, starting from a two-dimensional N=(4,4) gauged
linear sigma model describing Taub-NUT space. After dualizing the circle fiber,
we find that the smeared NS5-brane target space metric receives corrections
from multi-worldsheet instantons. These instantons are identified as
Nielsen-Olesen vortices. We show that their effect is to break the isometry of
the target space, localizing the NS5-brane at a point. The contribution from
the k-instanton sector is shown to be proportional to the weighted integral of
the Euler form over the k-vortex moduli space. The duality also predicts the,
previously unknown, asymptotic exponential decay coefficient of the BPS vortex
solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode
corrected. Reference added. v3: typo correcte
New instantons in the double-well potential
A new instanton solution is found in the quantum-mechanical double-well
potential with a four-fermion term. The solution has finite action and depends
on four fermionic collective coordinates. We explain why in general the
instanton action can depend on collective coordinates.Comment: 10 pages, clarifications and references adde
Instanton Calculus and SUSY Gauge Theories on ALE Manifolds
We study instanton effects along the Coulomb branch of an N=2 supersymmetric
Yang-Mills theory with gauge group SU(2) on Asymptotically Locally Euclidean
(ALE) spaces. We focus our attention on an Eguchi-Hanson gravitational
background and on gauge field configurations of lowest Chern class.Comment: 15 pages, LaTeX file. Extended version to be published in Physical
Review
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