The strong CP problem and higher dimensional gauge theories

Abstract

Abstract We discuss a natural scenario to solve the strong CP problem in the framework of the higher dimensional gauge theory. An axion-like field Ay has been built-in as the extra-space component of the higher dimensional gauge field. The coupling of Ay with gluons is attributed to the radiatively induced “Chern-Simons” (CS) term. We adopt a toy model with some unknown gauge symmetry U(1)X. The CS term is obtained in two ways: first by a concrete 1-loop calculation and next by use of the Fujikawa’s method to deal with the chiral anomaly in 4D space-time. The obtained results are identical, which implies that the radiative correction to the CS term is “1-loop exact” and is also free from UV-divergence even though the theory itself is non-renormalizable. As a novel feature of this scenario, such obtained CS term is no longer linear in the field Ay as in the usually discussed CS term in 5D space-time but a periodic function of Ay, since Ay has a physical meaning as the Wilson-loop phase. We argue how such novel feature of this scenario causes the modification of the ordinary solutions of the strong CP problem based on the axion fields.