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Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori. (English) Zbl 1058.58500

Summary: We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of \(d\)-dimensional tori with \(d=2,3,4\) are considered in full detail. SO\((d,d,Z)\)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.

MSC:

58B34 Noncommutative geometry (à la Connes)
81R60 Noncommutative geometry in quantum theory
81T75 Noncommutative geometry methods in quantum field theory
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[1] Banks, T.; Fischler, W.; Shenker, S.; Susskind, L., Phys. Rev. D, 55, 5112 (1997), hep-th/9610043
[2] N. Ishibashi, H. Kawai, I. Kitazawa, A. Tsuchiya, Nucl. Phys. B 492 (1997) 467; hep-th/9612115.; N. Ishibashi, H. Kawai, I. Kitazawa, A. Tsuchiya, Nucl. Phys. B 492 (1997) 467; hep-th/9612115.
[3] A. Connes, M. Douglas, A. Schwarz, JHEP 02 (1998) 003; hep-th/9711162.; A. Connes, M. Douglas, A. Schwarz, JHEP 02 (1998) 003; hep-th/9711162.
[4] A. Schwarz, Nucl. Phys. B 534 (1998) 720; hep-th/9805034.; A. Schwarz, Nucl. Phys. B 534 (1998) 720; hep-th/9805034.
[5] M. Rieffel, A. Schwarz, Morita equivalence of multidimensional noncommutative tori, q-alg/9803057.; M. Rieffel, A. Schwarz, Morita equivalence of multidimensional noncommutative tori, q-alg/9803057. · Zbl 0968.46060
[6] B. Morariu, B. Zumino, Super Yang-Mills on the noncommutative torus, hep-th/9807198.; B. Morariu, B. Zumino, Super Yang-Mills on the noncommutative torus, hep-th/9807198. · Zbl 0944.81051
[7] D. Brace, B. Morariu, A note on the BPS spectrum of the Matrix Model, hep-th/9810185.; D. Brace, B. Morariu, A note on the BPS spectrum of the Matrix Model, hep-th/9810185. · Zbl 0965.81079
[8] D. Brace, B. Morariu, B. Zumino, T-duality and Ramond-Ramond Backgrounds in the Matrix Model, hep-th/9811213.; D. Brace, B. Morariu, B. Zumino, T-duality and Ramond-Ramond Backgrounds in the Matrix Model, hep-th/9811213. · Zbl 0965.81079
[9] A. Konechny, A. Schwarz, BPS states on noncommutative tori and duality, to appear in Nucl. Phys. B; hep-th/9811159.; A. Konechny, A. Schwarz, BPS states on noncommutative tori and duality, to appear in Nucl. Phys. B; hep-th/9811159.
[10] C. Hofman, E. Verlinde, Gauge bundles and Born-Infeld on the noncommutative torus, hep-th/9810219.; C. Hofman, E. Verlinde, Gauge bundles and Born-Infeld on the noncommutative torus, hep-th/9810219. · Zbl 0943.81047
[11] N.A. Obers, B. Pioline, U-duality and M-Theory, hep-th/9809039.; N.A. Obers, B. Pioline, U-duality and M-Theory, hep-th/9809039.
[12] A.A. Kirillov, Geometric Quantization, Encyclopedia of Mathematical Sciences, vol. 4, p. 230.; A.A. Kirillov, Geometric Quantization, Encyclopedia of Mathematical Sciences, vol. 4, p. 230.
[13] A. Konechny, A. Schwarz, in preparation.; A. Konechny, A. Schwarz, in preparation.
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