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Morita equivalence and duality. (English) Zbl 1079.81066

Summary: It was shown by A. Connes, M. Douglas and A. Schwarz [J. High Energy Phys. 1998, No. 2, Paper No. 3 (1998; Zbl 1018.81052)] that one can compactify M(atrix) theory on a non-commutative torus \(T_{\theta}\). We prove that compactifications on Morita equivalent tori are in some sense physically equivalent. This statement can be considered as a generalization of non-classical SL\((2,\mathbb{Z})_{\mathbb{N}}\) duality conjectured by Connes, Douglas and Schwarz for compactifications on two-dimensional noncommutative tori.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
46L87 Noncommutative differential geometry
58B34 Noncommutative geometry (à la Connes)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Citations:

Zbl 1018.81052
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References:

[1] A. Connes, M. Douglas and A. Schwarz, Non-commutative geometry and Matrix theory: Compactification on tori, hep-th/9711162, JHEP XXXX.; A. Connes, M. Douglas and A. Schwarz, Non-commutative geometry and Matrix theory: Compactification on tori, hep-th/9711162, JHEP XXXX. · Zbl 1018.81052
[2] M. Blau and M. O’Laughlin, Aspects of \(U\); M. Blau and M. O’Laughlin, Aspects of \(U\)
[3] M. Rieffel and A. Schwarz, Morita equivalence of multidimensional non-commutative tori, qalg/9803057.; M. Rieffel and A. Schwarz, Morita equivalence of multidimensional non-commutative tori, qalg/9803057. · Zbl 0968.46060
[4] N. Nekrasov and A. Schwarz, Instantons on non-commutative \(R^4\); N. Nekrasov and A. Schwarz, Instantons on non-commutative \(R^4\)
[5] A. Astashkevich, N. Nekrasov and A. Schwarz, in preparation.; A. Astashkevich, N. Nekrasov and A. Schwarz, in preparation.
[6] Connes, A., Non-commutative Geometry (1994), Academic Press: Academic Press New York · Zbl 0933.46069
[7] Elliott, G. A., On the K-theory of the C*-algebras generated by a projective representation of a torsionfree discrete abelian group, (Operator Algebras and Group Representations (1984), Pitman: Pitman London), 157 · Zbl 0142.26103
[8] Banks, T.; Fishler, W.; Shenker, S.; Susskind, L., Phys. Rev. D, 55, 5112 (1997), hep-th /9610043
[9] Ishibashi, N.; Kawai, H.; Kitazava, I.; Tsuchiya, A., Nucl. Phys. B, 492, 467 (1997)
[10] A. Konechny and A. Schwarz, in preparation.; A. Konechny and A. Schwarz, in preparation.
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