288 research outputs found
A Note on the Hitchin System in a Background B-field
The space of solutions to the Hitchin equations on the dual torus with
punctures determines the Higgs branch of certain impurity theories. An
alternative description of this Higgs branch is provided, in terms of the
proper deformation of Hitchin system with deformation parameter given by a
-field. For the dual torus minus the singular points we construct explicit
solutions to the B-deformed Hitchin equations by reducing them to principal
chiral model equations and then using deformation quantization methods.Comment: 10 pages, harvmac file, no figures, added reference
N=2 String Geometry and the Heavenly Equations
In this paper we survey some of the relations between Plebanski description
of self-dual gravity through the heavenly equations and the physics (and
mathematics) of N=2 Strings. In particular we focus on the correspondence
between the infinite hierarchy in the ground ring structure of BRST operators
and its associated Boyer-Plebanski construction of infinite conserved
quantities in self-dual gravity. We comment on ``Mirror Symmetry'' in these
models and the large-N duality between topological N=4 gauge theories in two
dimensions and topological gravity in four dimensions. Finally D-branes in this
context are briefly outlined.Comment: 19+1 pages, 3 figures, corrected types, added references and
comments,to appear in the proceedings of the conference: Topics in
Mathematical Physics, General Relativity, and Cosmology, On the Occasion of
the 75th Birthday of Jerzy F. Plebanski (2002). September 17-20, 2002;
Cinvestav, Mexico Cit
Self-dual gravity via Hitchin's equations
In this work half-flat metrics are obtained from Hitchin's equations. The
SU Hitchin's equations are obtained and as a consequence of them, the
Husain-Park equation is found. Considering that the gauge group is SU,
some solutions associated to Liouville, sinh-Gordon and Painlev\'e III
equations are taken and, through Moyal deformations, solutions of the
SU Hitchin's equations are obtained. From these solutions,
hamiltonian vector fields are determined, which in turn are used to construct
the half-flat metrics. Following an approach of Dunajski, Mason and Woodhouse,
it is also possible to construct half-flat metrics on .Comment: 27+1 pages, no figure
Gauged WZW Models Via Equivariant Cohomology
The problem of computing systematically the gauge invariant extension of WZW
term through equivariant cohomology is addressed. The analysis done by Witten
in the two-dimensional case is extended to the four-dimensional ones. While
Cartan's model is used to find the anomaly cancelation condition. It is shown
that the Weil model is more appropriated to find the gauge invariant extension
of the WZW term. In the process we point out that Weil's and Cartan's models
are also useful to stress some connections with the abelian anomaly.Comment: 10 pages, no figure
Remarks on Noncommutative Solitons
In the first part of this work we consider an unstable non-BPS
Dp-\bar{Dp}-brane pair in Type II superstring theory. Turning on a background
NS-NS B-field (constant and nonzero along two spatial directions), we show that
the tachyon responsible for the unstability has a complex GMS solitonic
solution, which is interpreted as the low energy remnant of the resulting
D(p-2)-brane. In the second part, we apply these results to construct the
noncommutative soliton analogous of Witten's superconducting string. This is
done by considering the complex GMS soliton arising from the D3-\bar{D3}-brane
annihilation in Type IIB superstring theory. In the presence of left-handed
fermions, we apply the Weyl-Wigner-Moyal correspondence and the bosonization
technique to show that this object behaves like a superconducting wire.Comment: 24+1 pages, harvmac file, no figures, corrected typos, major
clarification
Lectures on Strings, D-branes and Gauge Theories
In these lectures we review the basic ideas of perturbative and
non-perturbative string theory. On the non-perturbative side we give an
introduction to D-branes and string duality. The elementary concepts of non-BPS
branes and noncommutative gauge theories are also discussed.Comment: 37+1 pages, LaTeX file, no figure
On the Berezin Description of Kahler Quotients
We survey geometric quantization of finite dimensional affine Kahler
manifolds. Its corresponding prequantization and the Berezin's deformation
quantization formulation, as proposed by Cahen et al., is used to quantize
their corresponding Kahler quotients. Equivariant formalism greatly facilitates
the description.Comment: 10 pages, latex file, no figures, minor clarifications and misprints
corrected, contribution to the Proceedings of the First Mexican Meeting on
Mathematical and Experimental Physics, Mexico Cit
A Reduced Model of Noncommutative S-brane Spectrum
CFT construction of S-branes describing the rolling and bouncing tachyons is
analyzed in the context of a -noncommutative deformation of
minisuperspace. Half s-brane and s-brane in the noncommutative minisuperspace
are analyzed and exact analytic solutions, involving the noncommutative
parameter and compatible with the boundary conditions at infinity, are
found. Comparison with the usual commutative minisuperspace is finally
performed.Comment: 19 pages, latex, 2 eps figures; v2/v3 references adde
A q-deformed Version of the Heavenly Equations
Using a -deformed Moyal algebra associated with the group of area
preserving diffeomorphisms of th two-dimensional torus , sdiff,
a -deformed version for the Heavenly equations is given. Finally, the
two-dimensional chiral version of Self-dual gravity in this -deformed
context is briefly discussed.Comment: 18 pages. LaTex, no figures, extended and corrected versio
Radiation Damping of a Yang-Mills Particle Revisited
The problem of a color-charged point particle interacting with a four
dimensional Yang-Mills gauge theory is revisited. The radiation damping is
obtained inspired in the Dirac's computation. The difficulties in the
non-abelian case were solved by using an ansatz for the Li\'enard-Wiechert
potentials, already used in the literature for finding solutions to the
Yang-Mills equations. Three non-trivial examples of radiation damping for the
non-abelian particle are discussed in detail.Comment: 33 pages, no figures, typos corrected, references adde
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