Comments on the Morita equivalence
It is known that the noncommutative Yang-Mills (YM) theory with periodical boundary conditions on a torus at a rational noncommutativity parameter value is Morita equivalent to the ordinary YM theory with twisted boundary conditions on a dual torus. We give a simple derivation of this fact. We describe the one-to-one correspondence between these two theories and the corresponding gauge invariant observables. In particular, we show that under the Morita map, the Polyakov loops in the ordinary YM theory are converted to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai, and Kitazawa.
KeywordsSpectroscopy Boundary Condition State Physics Field Theory Elementary Particle
Unable to display preview. Download preview PDF.
- 1.A. Connes, M. R. Douglas, and A. Schwarz, J. High Energy Phys. 9802, 003 (1998); hep-th/9711162.Google Scholar
- 2.N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999); hep-th/9908142.Google Scholar
- 5.G. Landi, F. Lizzi, and R. J. Szabo, hep-th/9912130.Google Scholar
- 9.A. Gonzalez-Arroyo, hep-th/9807108.Google Scholar
- 10.N. Ishibashi, S. Iso, H. Kawai, and Y. Kitazawa, hep-th/9910004.Google Scholar
- 11.J. Ambjorn, Y. M. Makeenko, J. Nishimura, and R. J. Szabo, hep-th/0002158; J. Ambjorn, Y. M. Makeenko, J. Nishimura, and R. J. Szabo, JHEP 9911, 029 (1999); hep-th/9911041.Google Scholar
- 12.J. Ambjorn, Y. M. Makeenko, J. Nishimura, and R. J. Szabo, hep-th/0004147.Google Scholar
- 13.B. Pioline and A. Schwarz, J. High Energy Phys. 9908, 021 (1999); hep-th/9908019.Google Scholar
- 14.R. Cai and N. Ohta, J. High Energy Phys. 0003, 009 (2000); hep-th/0001213.Google Scholar