• Corpus ID: 1279238

# 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}
}
• P. Ho
• Published 2 March 2000
• Mathematics
• arXiv: High Energy Physics - Theory
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

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## References

SHOWING 1-10 OF 19 REFERENCES

### Instantons on Noncommutative ℝ4, and (2,0) Superconformal Six Dimensional Theory

• Physics, Mathematics
• 1998
Abstract:We show that the resolution of moduli space of ideal instantons parameterizes the instantons on noncommutative ℝ4. This moduli space appears to be the Higgs branch of the theory of

### Noncommutative Geometry and Matrix Theory: Compactification on Tori

• Mathematics
• 1997
We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification

### Noncommutative geometry from strings and branes

• Mathematics
• 1999
Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a non-vanishing background B field. We

### Noncommutative Geometry and String Duality

• Mathematics
• 1999
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator

### D-branes and Deformation Quantization

In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract

### Noncommutative gauge theories in matrix theory

• Mathematics
• 1998
We present a general framework for matrix theory compactified on a quotient space ${\mathbf{R}}^{n}/\ensuremath{\Gamma},$ with \ensuremath{\Gamma} a discrete group of Euclidean motions in