Quantum field theories with compact noncommutative extra dimensions
Abstract
We study field theories on spaces with additional compact non-commutative dimensions. As an example, we study phi3 on Bbb R1,3 × Bbb T2θ using perturbation theory. The infrared divergences in the non-compact theory give rise to unusual dynamics for the mode of phi which is constant along the torus. Correlation functions involving this mode vanish. Moreover, we show that the spectrum of Kaluza-Klein excitations can be very different from the analogous commuting theory. There is an additional contribution to the Kaluza-Klein mass formula that resembles the contribution of winding states in string theory. We also consider the effect of noncommutativity on the four-dimensional Kaluza-Klein excitations of a six-dimensional gauge field.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- August 2000
- DOI:
- 10.1088/1126-6708/2000/08/029
- arXiv:
- arXiv:hep-th/0006160
- Bibcode:
- 2000JHEP...08..029G
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 15 pages, 4 Postscript figures, uses harvmac,references added, corrected typos in two equations, expanded discussion of gauge field zero mode dynamics