643 research outputs found
Lost equivalence of nonlinear sigma and models on noncommutative space
We show that the equivalence of nonlinear sigma and models which is
valid on the commutative space is broken on the noncommutative space. This
conclusion is arrived at through investigation of new BPS solitons that do not
exist in the commutative limit.Comment: 17 pages, LaTeX2
Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space
We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons
gauge theory coupled to a nonrelativistic complex adjoint matter on
noncommutative space. Soliton configurations of this model are related the
solutions of the chiral model on noncommutative plane. A generalized
Uhlenbeck's uniton method for the chiral model on noncommutative space provides
explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory
are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n'
should be an integer upon quantization. Toda and Liouville models are
generalized to noncommutative plane and the solutions are provided by the
uniton method. We also define affine Toda and sine-Gordon models on
noncommutative plane. Finally the first order moduli space dynamics of
Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur
New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model
Investigating the solitons in the non-commutative model, we have
found a new set of BPS solitons which does not have counterparts in the
commutative model.Comment: 8 pages, LaTeX2e, references added, improvements to discussions,
Version to be published in JHE
Unstable solitons on noncommutative tori and D-branes
We describe a class of exact solutions of super Yang-Mills theory on
even-dimensional noncommutative tori. These solutions generalize the solitons
on a noncommutative plane introduced in hep-th/0009142 that are conjectured to
describe unstable D2p-D0 systems. We show that the spectrum of quadratic
fluctuations around our solutions correctly reproduces the string spectrum of
the D2p-D0 system in the Seiberg-Witten decoupling limit. In particular the
fluctuations correctly reproduce the 0-0 string winding modes. For p=1 and p=2
we match the differences between the soliton energy and the energy of an
appropriate SYM BPS state with the binding energies of D2-D0 and D4-D0 systems.
We also give an example of a soliton that we conjecture describes branes of
intermediate dimension on a torus such as a D2-D4 system on a four-torus.Comment: 22 pages, Latex; v.2: references adde
Noncommutative Burgers Equation
We present a noncommutative version of the Burgers equation which possesses
the Lax representation and discuss the integrability in detail. We find a
noncommutative version of the Cole-Hopf transformation and succeed in the
linearization of it. The linearized equation is the (noncommutative) diffusion
equation and exactly solved. We also discuss the properties of some exact
solutions. The result shows that the noncommutative Burgers equation is
completely integrable even though it contains infinite number of time
derivatives. Furthermore, we derive the noncommutative Burgers equation from
the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is
an evidence for the noncommutative Ward conjecture. Finally, we present a
noncommutative version of the Burgers hierarchy by both the Lax-pair generating
technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato
theory and the integrability added, references added, version to appear in J.
Phys.
Noncommutative Vortex Solitons
We consider the noncommutative Abelian-Higgs theory and investigate general
static vortex configurations including recently found exact multi-vortex
solutions. In particular, we prove that the self-dual BPS solutions cease to
exist once the noncommutativity scale exceeds a critical value. We then study
the fluctuation spectra about the static configuration and show that the exact
non BPS solutions are unstable below the critical value. We have identified the
tachyonic degrees as well as massless moduli degrees. We then discuss the
physical meaning of the moduli degrees and construct exact time-dependent
vortex configurations where each vortex moves independently. We finally give
the moduli description of the vortices and show that the matrix nature of
moduli coordinates naturally emerges.Comment: 22 pages, 1 figure, typos corrected, a comment on the soliton size is
adde
Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
We study the noncommutative version of the extended ADHM construction in the
eight dimensional U(1) Yang-Mills theory. This construction gives rise to the
solutions of the BPS equations in the Yang-Mills theory, and these solutions
preserve at least 3/16 of supersymmetries. In a wide subspace of the extended
ADHM data, we show that the integer which appears in the extended ADHM
construction should be interpreted as the -brane charge rather than the
-brane charge by explicitly calculating the topological charges in the case
that the noncommutativity parameter is anti-self-dual. We also find the
relationship with the solution generating technique and show that the integer
can be interpreted as the charge of the -brane bound to the -brane
with the -field in the case that the noncommutativity parameter is
self-dual.Comment: 22 page
Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
We present a noncommutative generalization of Lax formalism of U(N) principal
chiral model in terms of a one-parameter family of flat connections. The Lax
formalism is further used to derive a set of parametric noncommutative
B\"{a}cklund transformation and an infinite set of conserved quantities. From
the Lax pair, we derive a noncommutative version of the Darboux transformation
of the model.Comment: 1+20 page
Calculating the Prepotential by Localization on the Moduli Space of Instantons
We describe a new technique for calculating instanton effects in
supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In
these situations the instantons are constrained and a potential is generated on
the instanton moduli space. Due to existence of a nilpotent fermionic symmetry
the resulting integral over the instanton moduli space localizes on the
critical points of the potential. Using this technology we calculate the one-
and two-instanton contributions to the prepotential of SU(N) gauge theory with
N=2 supersymmetry and show how the localization approach yields the prediction
extracted from the Seiberg-Witten curve. The technique appears to extend to
arbitrary instanton number in a tractable way.Comment: 24 pages, JHEP.cls, more references and extra discussion on N_F=2N
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