462 research outputs found
Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
We consider a complex vector bundle E endowed with a connection A over the
eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a
homogeneous space provided with a never integrable almost complex structure and
a family of SU(3)-structures. We establish an equivalence between G-invariant
solutions A of the Spin(7)-instanton equations on R^2 x G/H and general
solutions of non-Abelian coupled vortex equations on R^2. These vortices are
BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills
theory in ten dimensions compactified on the coset space G/H with an
SU(3)-structure. The novelty of the obtained vortex equations lies in the fact
that Higgs fields, defining morphisms of vector bundles over R^2, are not
holomorphic in the generic case. Finally, we introduce BPS vortex equations in
N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio
Low Threshold Parametric Decay Instabilities in ECRH experiments at toroidal devices
The experimental conditions leading to substantial reduction of
backscattering decay instability threshold in ECRH experiments in toroidal
devices are analyzed. It is shown that drastic decrease of threshold is
provided by non monotonic behaviour of plasma density, which is often observed
due to so-called density-pump-out effect or presence of magnetic islands, and
by poloidal magnetic field inhomogeniety making possible localization of ion
Bernstein decay waves. The corresponding ion Bernstein wave gain and the
parametric decay instability pump power threshold is calculated. The possible
experimental consequences of easy backscattering decay instability excitation
are discussed.Comment: 12 pages, 8 figures, submitted to Nuclear Fusio
Instantons and Yang-Mills Flows on Coset Spaces
We consider the Yang-Mills flow equations on a reductive coset space G/H and
the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces
G/H one can introduce geometric fluxes identified with the torsion of the spin
connection. The condition of G-equivariance imposed on the gauge fields reduces
the Yang-Mills equations to phi^4-kink equations on R. Depending on the
boundary conditions and torsion, we obtain solutions to the Yang-Mills
equations describing instantons, chains of instanton-anti-instanton pairs or
modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type
configurations are constructed as well. We also present explicit solutions to
the Yang-Mills flow equations and compare them with the Yang-Mills solutions on
R x G/H.Comment: 1+12 page
Super Calabi-Yau's and Special Lagrangians
We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and
show that the mirror can be recast in a form which depends only on the
superdimension and which is reminiscent of a generalized conifold. We discuss
its geometrical properties in comparison to the familiar conifold geometry. In
the second part of the paper examples of special-Lagrangian submanifolds are
constructed for a class of super Calabi-Yau's. We finally comment on their
infinitesimal deformations.Comment: 20 pages, no figures, latex; v2: references added; v3: minor
clarifications added, version published in JHE
A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
Super twistor space admits a certain (super) complex structure deformation
that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends
on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in
twistor string theory this deformation corresponds to augmenting N=4 super
Yang-Mills theory by a mass term for the left-chirality spinors. In this paper
we analyze this proposal in more detail. We calculate 4-particle scattering
amplitudes of fermions, gluons and scalars and show that they are supported on
holomorphic curves in the deformed twistor space.Comment: 52 pages, 15 figure
Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
We describe an infinite-dimensional algebra of hidden symmetries of N=4
supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a
generalization of the supertwistor correspondence. Using the latter, we
construct an infinite sequence of flows on the solution space of the N=4 SYM
equations. The dependence of the SYM fields on the parameters along the flows
can be recovered by solving the equations of the hierarchy. We embed the N=4
SYM equations in the infinite system of the hierarchy equations and show that
this SYM hierarchy is associated with an infinite set of graded symmetries
recursively generated from supertranslations. Presumably, the existence of such
nonlocal symmetries underlies the observed integrable structures in quantum N=4
SYM theory.Comment: 24 page
The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
In the recent paper hep-th/0502076, it was argued that the open topological
B-model whose target space is a complex (2|4)-dimensional mini-supertwistor
space with D3- and D1-branes added corresponds to a super Yang-Mills theory in
three dimensions. Without the D1-branes, this topological B-model is equivalent
to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the
latter with a holomorphic BF-type theory, we describe a twistor correspondence
between this theory and a supersymmetric Bogomolny model on R^3. The connecting
link in this correspondence is a partially holomorphic Chern-Simons theory on a
Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the
mini-supertwistor space. Along the way of proving this twistor correspondence,
we review the necessary basic geometric notions and construct action
functionals for the involved theories. Furthermore, we discuss the geometric
aspect of a recently proposed deformation of the mini-supertwistor space, which
gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually,
we present solution generating techniques based on the developed twistorial
description together with some examples and comment briefly on a twistor
correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio
Conformal Symmetries of the Self-Dual Yang-Mills Equations
We describe an infinite-dimensional Kac-Moody-Virasoro algebra of new hidden
symmetries for the self-dual Yang-Mills equations related to conformal
transformations of the 4-dimensional base space.Comment: 12 pages, Late
Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions
It was recently shown by Witten on the basis of several examples that the
topological B-model whose target space is a Calabi-Yau (CY) supermanifold is
equivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold.
Moreover, for the supertwistor space CP^{3|4} as target space, it has been
demonstrated that hCS theory on CP^{3|4} is equivalent to self-dual N=4 super
Yang-Mills (SYM) theory in four dimensions. We consider as target spaces for
the B-model the weighted projective spaces WCP^{3|2}(1,1,1,1|p,q) with two
fermionic coordinates of weight p and q, respectively - which are CY
supermanifolds for p+q=4 - and discuss hCS theory on them. By using twistor
techniques, we obtain certain field theories in four dimensions which are
equivalent to hCS theory. These theories turn out to be self-dual truncations
of N=4 SYM theory or of its twisted (topological) version.Comment: 12 pages; v2: minor clarification, 3 references added, published
versio
Matrix Models and D-branes in Twistor String Theory
We construct two matrix models from twistor string theory: one by dimensional
reduction onto a rational curve and another one by introducing noncommutative
coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment
on the interpretation of our matrix models in terms of topological D-branes and
relate them to a recently proposed string field theory. By extending one of the
models, we can carry over all the ingredients of the super ADHM construction to
a D-brane configuration in the supertwistor space P^(3|4). Eventually, we
present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio
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