IS CP A GAUGE-SYMMETRY

Abstract

Conventional solutions to the strong CP problem all require the existence of global symmetries. However, quantum gravity may destroy global symmetries, making it hard to understand why the electric dipole moment of the neutron (EDMN) is so small. We suggest here that CP is actually a discrete gauge symmetry, and is therefore not violated by quantum gravity. We show that four-dimensional CP can arise as a discrete gauge symmetry in theories with dimensional compactification, if the original number of Minkowski dimensions equals 8k + 1, 8k + 2 or 8k + 3, and if there are certain restrictions on the gauge group; these conditions are met by superstrings. CP may then be broken spontaneously below 10(9) GeV, explaining the observed CP violation in the kaon system without inducing a large EDMN. We discuss the phenomenology of such models, as well as the peculiar properties of cosmic ''CP strings'' which could be produced at the compactification scale. Such strings have the curious property that a particle carried around the string is turned into its CP conjugate. A single CP string renders four-dimensional space-time nonorientable.