Solving the strong CP problem without axions

We formulate general conditions under which the strong CP problem is solvedby spontaneous CP violation. Quark-mass matrix elements are polynomials in theCP-breaking order parameters, engineered such that their determinant is a realconstant. This scheme permits only a limited number of textures. Theseconditions can be realized in supersymmetric theories with CP as ananomaly-free local flavour symmetry, suggesting a unified solution to thestrong CP problem and the flavour puzzle. Our solution can be implemented usingeither modular invariance or a local U(1) symmetry. We presentmodular-invariant realizations where matter fields are assigned small modularweights ±2 (±1), utilising higher levels N=2 (N=3). Heavy quarksare in general not required, but their presence allows for models where coloredparticles fill non-singlet representations of the flavour group.

Further reading#

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