×
Konechny, Anatoly; Schwarz, Albert

BPS states on non-commutative tori and duality. (English) Zbl 0949.58004

Nucl. Phys., B 550, No. 3, 561-584 (1999).
Summary: We study gauge theories on non-commutative tori. It has been proved that Morita equivalence of non-commutative tori leads to a physical equivalence (SO\((d,d\mathbb{Z})\)-duality) of the corresponding gauge theories (A. Schwarz, 1998). We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the SO\((d,d\mathbb{Z})\)-duality. The relation of our results with those of recent calculations is discussed.

Cited in 7 Documents

MSC:

58B99 Infinite-dimensional manifolds
81T99 Quantum field theory; related classical field theories

Keywords:

non-commutative tori; energy spectrum; maximally supersymmetric BPS states
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Connes, A.; Douglas, M.; Schwarz, A., Non-commutative geometry and Matrix theory: compactification on tori, JHEP 02, 003 (1998), hep-th/9711162 · Zbl 1018.81052
[2] Rieffel, M. A., Morita equivalence for operator algebras, (Kadison, R. V., Operator Algebras and Applications. Operator Algebras and Applications, Proc. Symp. Pure Math., 38 (1982), Amer. Math. Soc: Amer. Math. Soc Providence) · Zbl 0541.46044
[3] Elliott, G. A., On the K-theory of the \(C^∗- algebra\), generated by a projective representation of a torsion-free discrete abelian group, (Operator Algebras and Group Representations (1984), Pitman: Pitman London), 157-184 · Zbl 0542.46030
[4] Connes, A.; Rieffel, M., Contemp. Math. Oper. Algebra. Math. Phys., 62 (1987), AMS · Zbl 0633.46069
[5] Schwarz, A., Morita equivalence and duality, Nucl. Phys. B, 534, 720 (1998), hep-th/9805034 · Zbl 1079.81066
[6] M. Rieffel and A. Schwarz, Morita equivalence of multidimensional non-commutative tori, q-alg/9803057.; M. Rieffel and A. Schwarz, Morita equivalence of multidimensional non-commutative tori, q-alg/9803057. · Zbl 0968.46060
[7] P.M. Ho, Twisted bundle on quantum torus and BPS states in Matrix theory, hep-th/9803166.; P.M. Ho, Twisted bundle on quantum torus and BPS states in Matrix theory, hep-th/9803166.
[8] B. Morariu and B. Zumino, Super Yang-Mills on the non-commutative torus, hep-th/9807198.; B. Morariu and B. Zumino, Super Yang-Mills on the non-commutative torus, hep-th/9807198.
[9] D. Brace, B. Morariu and B. Zumino, Dualities of the Matrix model from \(T\); D. Brace, B. Morariu and B. Zumino, Dualities of the Matrix model from \(T\) · Zbl 0944.81051
[10] D. Brace and B. Morariu, A note on the BPS spectrum of the Matrix model, hep-th/9810185 (two versions).; D. Brace and B. Morariu, A note on the BPS spectrum of the Matrix model, hep-th/9810185 (two versions). · Zbl 0965.81079
[11] C. Hofman and E. Verlinde, U-duality of Born-Infeld on the non-commutative two-torus, hep-th/9810116.; C. Hofman and E. Verlinde, U-duality of Born-Infeld on the non-commutative two-torus, hep-th/9810116. · Zbl 0949.81068
[12] C. Hofman and E. Verlinde, Gauge bundles and Born-Infeld on the non-commutative torus; hep-th/9810219.; C. Hofman and E. Verlinde, Gauge bundles and Born-Infeld on the non-commutative torus; hep-th/9810219. · Zbl 0943.81047
[13] A. Konechny and A. Schwarz, Supersymmetry algebra and BPS states of super Yang-Mills theories on non-commutative tori, to appear in Phys. Lett. B; hep-th/9901077.; A. Konechny and A. Schwarz, Supersymmetry algebra and BPS states of super Yang-Mills theories on non-commutative tori, to appear in Phys. Lett. B; hep-th/9901077.
[14] W. Taylor, Lectures on D-branes, Gauge Theory and M(atrices), hep-th/9801182.; W. Taylor, Lectures on D-branes, Gauge Theory and M(atrices), hep-th/9801182.
[15] A.A. Kirillov, Geometric Quantization, Encyclopedia of Mathematical Sciences, Vol. 4, 230.; A.A. Kirillov, Geometric Quantization, Encyclopedia of Mathematical Sciences, Vol. 4, 230.
[16] A. Astashkevich and A. Schwarz, Classification of projective modules with constant curvature connection over non-commutative tori.; A. Astashkevich and A. Schwarz, Classification of projective modules with constant curvature connection over non-commutative tori. · Zbl 0996.46031
[17] Igusa, Jun-ichi, Theta Functions (1972), Chapter II, Section 4, Lemma 5 · Zbl 0251.14016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.