120 research outputs found
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
Particle phenomenology on noncommutative spacetime
We introduce particle phenomenology on the noncommutative spacetime called
the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is
constrained from the CPT violation measurements in system
and difference of . The system
provides an upper bound on the length scale of spacetime noncommutativity of
the order of , corresponding to a lower energy bound
of the order of . The difference of constrains the noncommutativity length scale to be of the order of
, corresponding to a lower energy bound of the order
of .
We also present the phenomenology of the electromagnetic interaction of
electrons and nucleons at the tree level in the noncommutative spacetime. We
show that the distributions of charge and magnetization of nucleons are
affected by spacetime noncommutativity. The analytic properties of
electromagnetic form factors are also changed and it may give rise to
interesting experimental signals.Comment: 10 pages, 3 figures. Published versio
Notes on Noncommutative Instantons
We study in detail the ADHM construction of U(N) instantons on noncommutative
Euclidean space-time R_{NC}^4 and noncommutative space R_{NC}^2 x R^2. We point
out that the completeness condition in the ADHM construction could be
invalidated in certain circumstances. When this happens, regular instanton
configuration may not exist even if the ADHM constraints are satisfied. Some of
the existing solutions in the literature indeed violate the completeness
condition and hence are not correct. We present alternative solutions for these
cases. In particular, we show for the first time how to construct explicitly
regular U(N) instanton solutions on R_{NC}^4 and on R_{NC}^2 x R^2. We also
give a simple general argument based on the Corrigan's identity that the
topological charge of noncommutative regular instantons is always an integer.Comment: Regular instanton solutions are now explicitly constructed also for
the case of space-space noncommutativit
Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
We construct a supersymmetry and global symmetry
preserving deformation of the type IIB matrix model. This model, without
orbifold projection, serves as a nonperturbative regularization for
supersymmetric Yang-Mills theory in four Euclidean dimensions.
Upon deformation, the eigenvalues of the bosonic matrices are forced to reside
on the surface of a hypertorus. We explicitly show the relation between the
noncommutative moduli space of the deformed matrix theory and the Brillouin
zone of the emergent lattice theory. This observation makes the transmutation
of the moduli space into the base space of target field theory clearer. The
lattice theory is slightly nonlocal, however the nonlocality is suppressed by
the lattice spacing. In the classical continuum limit, we recover the
SYM theory. We also discuss the result in terms of D-branes and
interpret it as collective excitations of D(-1) branes forming D3 branes.Comment: Version 2: Extended discussion of moduli space, added a referenc
Noncommutative Standard Model: Model Building
A noncommutative version of the usual electro-weak theory is constructed. We
discuss how to overcome the two major problems: 1) although we can have
noncommutative U(n) (which we denote by ) gauge theory we cannot
have noncommutative SU(n) and 2) the charges in noncommutative QED are
quantized to just . We show how the problem with charge quantization,
as well as with the gauge group, can be resolved by taking gauge group and reducing the extra U(1)
factors in an appropriate way. Then we proceed with building the noncommutative
version of the standard model by specifying the proper representations for the
entire particle content of the theory, the gauge bosons, the fermions and
Higgs. We also present the full action for the noncommutative Standard Model
(NCSM). In addition, among several peculiar features of our model, we address
the {\it inherent} CP violation and new neutrino interactions.Comment: Latex file, 46 pages, no figures, v2: Higgsac symmetry reduction
arguments improved, Appendices and Ref. adde
Algebraic deformations of toric varieties I. General constructions
We construct and study noncommutative deformations of toric varieties by
combining techniques from toric geometry, isospectral deformations, and
noncommutative geometry in braided monoidal categories. Our approach utilizes
the same fan structure of the variety but deforms the underlying embedded
algebraic torus. We develop a sheaf theory using techniques from noncommutative
algebraic geometry. The cases of projective varieties are studied in detail,
and several explicit examples are worked out, including new noncommutative
deformations of Grassmann and flag varieties. Our constructions set up the
basic ingredients for thorough study of instantons on noncommutative toric
varieties, which will be the subject of the sequel to this paper.Comment: 54 pages; v2: Presentation of Grassmann and flag varieties improved,
minor corrections; v3: Presentation of some parts streamlined, minor
corrections, references added; final version to appear in Advances in
Mathematic
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