# Twisted Bundle on Noncommutative Space and U(1) Instanton

@article{Ho2000TwistedBO, title={Twisted Bundle on Noncommutative Space and U(1) Instanton}, author={Pei-Ming Ho}, journal={arXiv: High Energy Physics - Theory}, year={2000} }

We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton solution of Nekrasov and Schwarz is such an example. As a mathematical motivation for not excluding such bundles, we find gauge transformations by which a bundle with constant dimension can be equivalent to a bundle with non-constant dimension.

## 22 Citations

### “Topological” Charge of U(1) Instantons on Noncommutative R4

- Mathematics, Physics
- 2000

Non-singular instantons are shown to exist on noncommutative R 4 even in U(1) gauge theory. Their existence is primarily due to the noncommutativity of the coordinates. The integer instanton number…

### Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

- Mathematics, Physics
- 2000

Abstract. An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows…

### Noncommutative solitons in open N = 2 string theory

- Physics
- 2001

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…

### Noncommutative 't Hooft instantons

- Mathematics
- 2001

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…

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

- Mathematics
- 2001

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…

### Fluxons and exact BPS solitons in non-commutative gauge theory

- Mathematics
- 2000

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…

### Noncommutative Solitons and D-branes

- Mathematics
- 2003

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.

### Noncommutative instantons on d = 2 n planes from matrix models

- Mathematics

In the case of an invertible coordinate commutator matrix θij, we derive a general instanton solution of the noncommutative gauge theories on d = 2n planes given in terms of n oscillators.

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