Quantum Field Theories With Compact Noncommutative Extra Dimensions

TL;DR

This paper investigates quantum field theories on spaces with compact noncommutative extra dimensions, revealing unique infrared behaviors, altered Kaluza-Klein spectra, and string-like contributions to mass formulas.

Contribution

It provides the first detailed analysis of how noncommutative compact dimensions affect field theory dynamics and spectra, including novel infrared effects and modifications to Kaluza-Klein modes.

Findings

Infrared divergences lead to unusual dynamics for constant modes.

Correlation functions involving constant modes vanish.

Kaluza-Klein spectra are significantly altered, with string-like mass contributions.

Abstract

We study field theories on spaces with additional compact noncommutative dimensions. As an example, we study \phi^3 on R^{1,3}\times T^{2}_\theta using perturbation theory. The infrared divergences in the noncompact 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.