994 research outputs found
How to find discrete contact symmetries
This paper describes a new algorithm for determining all discrete contact
symmetries of any differential equation whose Lie contact symmetries are known.
The method is constructive and is easy to use. It is based upon the observation
that the adjoint action of any contact symmetry is an automorphism of the Lie
algebra of generators of Lie contact symmetries. Consequently, all contact
symmetries satisfy various compatibility conditions. These conditions enable
the discrete symmetries to be found systematically, with little effort
A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies
A family of mappings from the solution spaces of certain generalized
Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system on R^{2,2} is
described. This provides an extension of the well-known relationship between
self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov
type
Toric anti-self-dual Einstein metrics via complex geometry
Using the twistor correspondence, we give a classification of toric
anti-self-dual Einstein metrics: each such metric is essentially determined by
an odd holomorphic function. This explains how the Einstein metrics fit into
the classification of general toric anti-self-dual metrics given in an earlier
paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen
(math.DG/0105263), who describe where the Einstein metrics appear amongst the
Joyce spaces, leading to a different classification. Taking the twistor
transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page
Quantisation of twistor theory by cocycle twist
We present the main ingredients of twistor theory leading up to and including
the Penrose-Ward transform in a coordinate algebra form which we can then
`quantise' by means of a functorial cocycle twist. The quantum algebras for the
conformal group, twistor space CP^3, compactified Minkowski space CMh and the
twistor correspondence space are obtained along with their canonical quantum
differential calculi, both in a local form and in a global *-algebra
formulation which even in the classical commutative case provides a useful
alternative to the formulation in terms of projective varieties. We outline how
the Penrose-Ward transform then quantises. As an example, we show that the
pull-back of the tautological bundle on CMh pulls back to the basic instanton
on S^4\subset CMh and that this observation quantises to obtain the
Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the
tautological bundle on our \theta-deformed CMh. We likewise quantise the
fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed
CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae
for classical and quantum CP^
Calorons, Nahm's equations on S^1 and bundles over P^1xP^1
The moduli space of solutions to Nahm's equations of rank (k,k+j) on the
circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent
to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity
with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit
matrix description of these spaces is given by a monad constructio
On the Strong Coupling Limit of the Faddeev-Hopf Model
The variational calculus for the Faddeev-Hopf model on a general Riemannian
domain, with general Kaehler target space, is studied in the strong coupling
limit. In this limit, the model has key similarities with pure Yang-Mills
theory, namely conformal invariance in dimension 4 and an infinite dimensional
symmetry group. The first and second variation formulae are calculated and
several examples of stable solutions are obtained. In particular, it is proved
that all immersive solutions are stable. Topological lower energy bounds are
found in dimensions 2 and 4. An explicit description of the spectral behaviour
of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the
stability of this map in the full Faddeev-Hopf model is proved.Comment: 21 pages, 0 figure
The self-dual gauge fields and the domain wall fermion zero modes
A new type of gauge fixing of the Coulomb gauge domain wall fermion system
that reduces the fluctuation of the effective running coupling and the
effective mass of arbitrary momentum direction including the region outside the
cylinder cut region is proposed and tested in the
gauge configurations of RBC/UKQCD collaboration.
The running coupling at the lowest momentum point does not show infrared
suppression and compatible with the experimental data extracted from the JLab
collaboration. The source of the fluctuation of the effective mass near
momentum 0.6GeV region is expected to be due to the domain wall fermion
zero modes.Comment: 12 pages 2 figures, extended arguments and references adde
Supersymmetric Gauge Theories in Twistor Space
We construct a twistor space action for N=4 super Yang-Mills theory and show
that it is equivalent to its four dimensional spacetime counterpart at the
level of perturbation theory. We compare our partition function to the original
twistor-string proposal, showing that although our theory is closely related to
string theory, it is free from conformal supergravity. We also provide twistor
actions for gauge theories with N<4 supersymmetry, and show how matter
multiplets may be coupled to the gauge sector.Comment: 23 pages, no figure
Beyond the Syndrome: Extensive Congenital Abnormalities in an Infant With Trisomy 21
Herein we discuss the clinical course and subsequent autopsy of a female infant with trisomy 21 with balanced Rastelli Type ?C? complete atrioventricular septal defect (AVSD), tetralogy of Fallot and right aortic arch with mirror image branching pattern who underwent a palliative right modified Blalock-Taussig-Thomas shunt (mBTTS) for hypoxemia from progressive right ventricular outflow tract obstruction. The baby was found to have multiple concomitant pathologic findings not typically seen with this constellation of cardiac anatomy. Autopsy revealed significant abdominal adhesions with near-complete stenosis of the transverse colon. In addition, the infant was found to have significantly elongated villi within the small and large bowel and a relatively large collagenous polyp in the small bowel. The decedent also had an abnormal tracheal bronchus, characterized by an additional superior right-sided bronchus, which is an extremely rare abnormality. Her clinical course was complicated by severe pulmonary hypertensive arteriolar changes out of proportion to what would be typical for her age, trisomy 21 status, and degree of left to right intracardiac shunting. Furthermore, she had refractory anasarca and recurrent chylous pleural effusions without gross lymphatic abnormalities that may have been secondary to systemic capillary leak syndrome (SCLS) versus severe pulmonary hypertension. Due to the aforementioned findings, the family elected for comfort care and the baby expired shortly after extubation. Overall, the infant had multiple, rare coexisting congenital abnormalities that likely represents an extreme phenotype of trisomy 21 that has not been described in the literature to date
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
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