Seiberg-Witten transforms of noncommutative solitons

@article{Hashimoto2001SeibergWittenTO,
  title={Seiberg-Witten transforms of noncommutative solitons},
  author={Koji Hashimoto and Hirosi Ooguri},
  journal={Physical Review D},
  year={2001},
  volume={64},
  pages={106005}
}
We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the… 
View PDF on arXiv
41 Citations
Highly Influential Citations
2
Background Citations
13
Methods Citations
5

41 Citations

Seiberg–Witten monopole equations on noncommutative R4

It is well known that, due to vanishing theorems, there are no nontrivial finite action solutions to the Abelian Seiberg–Witten (SW) monopole equations on Euclidean four-dimensional space R4. We show…

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…

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 [7] that are…

Noncommutative Solitons and D-branes

This thesis focuses on noncommutative instantons and monopoles and study various aspects of the exact solutions by using Atiyah-Drinfeld-Hitchin-Manin (ADHM) and Nahm constructions, and proposes noncommuter extensions of integrable systems and soliton theories in lower dimensions in collaboration with Kouichi Toda.

ALE spaces from noncommutative U(1) instantons via exact Seiberg–Witten map

Noncommutative Instantons via Dressing and Splitting Approaches

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the…

Noncommutative multi solitons in (2+1)-dimensions

The study of non-commutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in…

Noncommutative extended waves and soliton - like configurations in N=2 string theory

The Seiberg–Witten limit of fermionic N = 2 string theory with nonvanishing B-field is governed by noncommutative self-dual Yang–Mills theory (ncSDYM) in 2+2 dimensions. Conversely, the self-duality…

Noncommutative 't Hooft instantons

We employ the twistor approach to the construction of U(2) multi-instantons a la 't Hooft on non-commutative 4. The non-commutative deformation of the Corrigan-Fairlie-'t Hooft-Wilczek ansatz is…

Exact Seiberg–Witten map, induced gravity and topological invariants in non-commutative field theories

68 References

Unstable solitons in noncommutative gauge theory

We find a class of exact solutions of noncommutative gauge theories corresponding to unstable non-BPS solitons. In the two-dimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find…

Solitons in noncommutative gauge theory

We present a unified treatment of classical solutions of non-commutative gauge theories. We find all solutions of the non-commutative Yang-Mills equations of motion in 2 dimensions; and show that…

Projector equivalences in K theory and families of non-commutative solitons

Projector equivalences used in the definition of the K-theory of operator algebras are shown to lead to generalizations of the solution generating technique for solitons in NC field theories, which…

Noncommutative Monopole at the Second Order in θ

We study the noncommutative U(2) monopole solution at the second order in the noncommutativity parameter \theta^{ij}. We solve the BPS equation in noncommutative super Yang-Mills theory to…

On exact noncommutative BPS solitons

We construct new exact BPS solitons in various noncommutative gauge theories by the ``gauge'' transformation of known BPS solitons. This ``gauge'' transformation introduced by Harvey, Kraus and…

Instantons on Noncommutative R 4 and Projection Operators

The noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz, is carefully studied. Noncommutative R is described by an algebra of operators acting in a…

Ramond-Ramond Couplings of Noncommutative D-branes

Fluxons and exact BPS solitons in non-commutative gauge theory

We show that the fluxon solution of the non-commutative gauge theory and its variations are obtained by the soliton generation method recently given by J. A. Harvey, P. Kraus and F. Larsen…

On Noncommutative Multi-Solitons

Abstract: We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is…

Noncommutative solitons in open N = 2 string theory

Coincident D2-branes in open N = 2 fermionic string theory with a B-field background yield an integrable modified U(n) sigma model on noncommutative 2,1. This model provides a showcase for an…
...