A spontaneously broken modular CP symmetry can force the quark mass determinant to be real, solving the strong CP problem without an axion.
Supersymmetric Solutions to the Strong CP Problem
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abstract
It is argued that in the context of supersymmetry, the Strong CP Problem is most naturally seen as an aspect (particularly severe) of the whole complex of flavor-violating and CP-violating problems of supersymmetry. It is shown that certain approaches to solving these flavor problems also allow simple solutions to the Strong CP Problem. The idea of ``flavor alignment" suggested by Nir and Seiberg allows not only flavor violation to be controlled but supersymmetric contributions to the theta parameter to be made acceptably small. Another approach to the flavor-violation problem, namely low-energy supersymmetry breaking, allows another class of solutions to the Strong CP Problem to be viable.
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Solving the strong CP problem
A spontaneously broken modular CP symmetry can force the quark mass determinant to be real, solving the strong CP problem without an axion.