1,221 research outputs found
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
Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter
Using standard field theory techniques we compute perturbative and instanton
contributions to the Coulomb branch of three-dimensional supersymmetric QCD
with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with
one massless flavor, we confirm the proposal of Seiberg and Witten that the
Coulomb branch is the double-cover of the centered moduli space of two BPS
monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass
term, we show that the asymptotic metric on the Coulomb branch coincides with
the metric on Dancer's deformation of the monopole moduli space. For the N=2
theory with flavors, we compute the one-loop corrections to the metric
and complex structure on the Coulomb branch. We then determine the
superpotential including one-loop effects around the instanton background.
These calculations provide an explicit check of several results previously
obtained by symmetry and holomorphy arguments.Comment: 24 pages, Late
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
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
Another Leigh-Strassler deformation through the Matrix model
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to
obtain the effective superpotential for a certain deformation of N=4 SYM
discovered by Leigh and Strassler. An exact solution to the matrix model
Lagrangian is found and is expressed in terms of elliptic functions.Comment: 15 pages,2 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
A New 2d/4d Duality via Integrability
We prove a duality, recently conjectured in arXiv:1103.5726, which relates
the F-terms of supersymmetric gauge theories defined in two and four dimensions
respectively. The proof proceeds by a saddle point analysis of the
four-dimensional partition function in the Nekrasov-Shatashvili limit. At
special quantized values of the Coulomb branch moduli, the saddle point
condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain
which coincides with the F-term equation of the dual two-dimensional theory.
The on-shell values of the superpotential in the two theories are shown to
coincide in corresponding vacua. We also identify two-dimensional duals for a
large set of quiver gauge theories in four dimensions and generalize our proof
to these cases.Comment: 19 pages, 2 figures, minor corrections and references adde
Scattering of Giant Holes
We study scalar excitations of high spin operators in N=4 super Yang-Mills
theory, which are dual to solitons propagating on a long folded string in AdS_3
x S^1. In the spin chain description of the gauge theory, these are associated
to holes in the magnon distribution in the sl(2,R) sector. We compute the
all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading
orders at weak and strong coupling. The worldsheet S-matrix of solitonic
excitations on the GKP string is calculated using semiclassical quantization.
We find an exact agreement between the gauge theory and string theory results.Comment: 13 pages. v2: minor corrections, references adde
The Quantum Dynamics of Heterotic Vortex Strings
We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge
group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2)
supersymmetry, but this is broken by quantum effects. We show how the pattern
of supersymmetry breaking and restoration on the worldsheet captures the
quantum dynamics of the underlying 4d theory. We also find qualitative matching
of the meson spectrum in 4d and the spectrum on the worldsheet.Comment: 13 page
Heterotic Vortex Strings
We determine the low-energy N=(0,2) worldsheet dynamics of vortex strings in
a large class of non-Abelian N=1 supersymmetric gauge theories.Comment: 44 pages, 3 figures. v2: typos corrected, reference adde
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