Abstract
Following the construction of the projection operators on T 2 presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold T 2/G(G=Z N , N=2, 3, 4, 6) which correspond to a set of solitons on T 2/Z N in noncommutative field theory. In this way, we derive an explicit form of projector on T 2/Z 6 as an example. We also construct a complete set of projectors on T 2/Z N by series expansions for integral case.
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References
Connes, A.: Non-commutative Geometry, Academic Press, New York, 1994.
Landi, G.: An introduction to non-commutative space and their geometry, hep-th/ 9701078; Varilly, J.: An introduction to non-commutative geometry, physics/9709045.
Madore, J.: An Introduction to Non-commutative Differential Geometry and its Physical Applications, 2nd edn, Cambridge Univ. Press, 1999.
Connes, A., Douglas, M. and Schwartz, A.: Matrix theory compactification on Tori, J. High Energy Phys. 9802 (1998) 003, hep-th/9711162; M. Dougals, C. Hull, JHEP 9802 (1998) 008, hep-th/9711165.
Seiberg, N. and Witten, E.: String theory and non-commutative geometry, J. High Energy Phys. 9909 (1999), 032, hep-th/9908142; Schomerus, V.: D-branes and deformation quantization, J.High Energy Phys. 9906 (1999), 030.
Witten, E. Noncommutative geometry and string field theory, Nuclear Phys. B 268 (1986), 253.
Laughlin, R. B.: In: R. Prange and S. Girvin (eds), The quantum Hall Effect, Springer, New York, 1987, p233.
Susskind, L.: hep-th/0101029; Hu, J. P. and Zhang, S. C.: cond-mat/0112432.
Gopakumar, R., Headrick, M. and Spradin, M.: On noncommutative multi-solitons, hepth/ 0103256.
Martinec, E. J. and Moore, G.: Noncommutative solitons on orbifolds, hep-th/0101199.
Gross, D. J. and Nekrasov, N. A.: Solitons in noncommutative gauge theory, hep-th/ 0010090; Douglas, M. R. and Nekrasov, N. A.: Noncommutative field theory, hep-th/ 0106048.
Gopakumar, R., Minwalla, S. and Strominger, A.: Noncommutative soliton, J. High Energy Phys. 005 (2000), 048, hep-th/0003160.
Harvey, J.: Komaba lectures on noncommutative solitons and D-branes, hep-th/0102076; Harvey, J. A., Kraus, P. and Larsen, F.: J. High Energy Phys. 0012 (200), 024, hep-th/ 0010060; Hamanaka, M. and Terashima, S.: On exact noncommutative BPS solitons, J. High Energy Phys. 0103 (2001), 034, hep-th/0010221.
Rieffel, M.: Pacific J. Math. 93 (1981), 415.
Boca, F. P.: Comm. Math. Phys. 202 (1999), 325.
Konechny, A. and Schwartz, A.: Compactification of M(atrix) theory on noncommutative toroidal orbifolds Nuclear Phys.B 591, 667 (2000), hep-th/9912185; Module spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds, J.High Energy Phys. 0009 (2000), 005, hep-th/0005167.
Walters, S.: Projective modules over noncommutative sphere, J. London Math. Soc. 51 (1995), 589; Chern characters of Fourier modules, Canad. J. Math. 52 (2000), 633.
Bacry, H., Grossman, A. and Zak, J.: Phys. Rev. B 12 (1975), 1118.
Zak, J.: In H. Ehrenreich, F. Seitz and D. Turnbull (eds). Solid State Physics, Academic Press, New York, 1972.
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Hou, By., Shi, Kj. & Yang, Zy. Solitons on Noncommutative Orbifold T 2/Z N . Letters in Mathematical Physics 61, 205–220 (2002). https://doi.org/10.1023/A:1021294221710
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DOI: https://doi.org/10.1023/A:1021294221710