We show that a recently proposed solution to the hierarchy problem simultaneously solves the strong CP problem, without requiring an axion or any further new physics. Consistency of black hole physics implies a nontrivial relation between the number of particle species and particle masses, so that with approximately 10(32) copies of the standard model, the TeV scale is naturally explained. At the same time, as shown here, this setup predicts a typical expected value of the strong-CP parameter in QCD of theta approximately 10(-9). This strongly motivates a more sensitive measurement of the neutron electric dipole moment.
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