The Strong CP Problem, String Theory and the Nelson-Barr Mechanism

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We review recent work on the strong CP problem in the context of realistic string-inspired models. We discuss the various solutions, review the conjecture that CP is generally a gauged discrete symmetry in string theory and then consider models of the Nelson-Barr type. We note that squark non-degeneracy spoils the Nelson-Barr structure at the one loop level. We stress that string theory expectations, as well as naturalness arguments, make it very difficult to avoid the constraints on non-degeneracy.
preprint SCIPP 93/14; 10 pages, latex format, uses epsf.tex for 2 figures, submitted separately via `uufiles'

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