204 research outputs found
On the ADHM construction of noncommutative U(2) k-instanton
The basic objects of the ADHM construction are reformulated in terms of
elements of the algebra of the noncommutative
space. This new formulation of the ADHM construction makes possible the
explicit calculus of the U(2) instanton number which is shown to be the product
of a trace of finite rank projector of the Fock representation space of the
algebra times a noncommutative version of the winding number.Comment: 22 pages, new version to appear in Phys. Rev.
String solitons in the M5-brane worldvolume with a Nambu-Poisson structure and Seiberg-Witten map
We analyze BPS equations for string-like configurations derived from the
M5-brane worldvolume action with a Nambu-Poisson structure constructed in
arXiv:0804.3629, arXiv:0805.2898. We solve the BPS equations up to the first
order in the parameter which characterizes the strength of the
Nambu-Poisson bracket. We compare our solutions to previously constructed BPS
string solitons in the conventional description of M5-brane in a constant
three-form background via Seiberg-Witten map, and find agreement.Comment: v2: minor corrections, the title slightly changed. 10 pages. v3: some
clarifying comment
Instanton Number of Noncommutative U(n) gauge theory
We show that the integral of the first Pontrjagin class is given by an
integer and it is identified with instanton number of the U(n) gauge theory on
noncommutative . Here the dimension of the vector space that
appear in the ADHM construction is called Instanton number. The calculation is
done in operator formalism and the first Pontrjagin class is defined by
converge series. The origin of the instanton number is investigated closely,
too.Comment: 6 color figures, 27 pages, some comments and references are
added,typos fixe
Point-Like Graviton Scattering in Plane-Wave Matrix Model
In a plane-wave matrix model we discuss a two-body scattering of gravitons in
the SO(3) symmetric space. In this case the graviton solutions are point-like
in contrast to the scattering in the SO(6) symmetric space where spherical
membranes are interpreted as gravitons. We concentrate on a configuration in
the 1-2 plane where a graviton rotates with a constant radius and the other one
elliptically rotates. Then the one-loop effective action is computed by using
the background field method. As the result, we obtain the 1/r^7-type
interaction potential, which strongly suggests that the scattering in the
matrix model would be closely related to that in the light-front
eleven-dimensional supergravity.Comment: 17 pages, 1 figure, LaTeX, v2) references adde
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
cas
Supersymmetric reduced models with a symmetry based on Filippov algebra
Generalizations of the reduced model of super Yang-Mills theory obtained by
replacing the Lie algebra structure to Filippov -algebra structures are
studied. Conditions for the reduced model actions to be supersymmetric are
examined. These models are related with what we call \{cal N}_{min}=2 super
-brane actions.Comment: v3: In the previous versions we overlooked that Eq.(3.9) holds more
generally, and missed some supersymmetric actions. Those are now included and
modifications including a slight change in the title were made accordingly.
1+18 page
Non-Commutative Instantons and the Seiberg-Witten Map
We present several results concerning non-commutative instantons and the
Seiberg-Witten map. Using a simple ansatz we find a large new class of
instanton solutions in arbitrary even dimensional non-commutative Yang-Mills
theory. These include the two dimensional ``shift operator'' solutions and the
four dimensional Nekrasov-Schwarz instantons as special cases. We also study
how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal
Seiberg-Witten map is shown to take a very simple form in operator language,
and this result is used to give a commutative description of non-commutative
instantons. The instanton is found to be singular in commutative variables.Comment: 26 pages, AMS-LaTeX. v2: the formula for the commutative description
of the Nekrasov-Schwarz instanton corrected (sec. 4). v3: minor correction
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