Spontaneous CP violation and the strong CP problem in left-right symmetric theories

We study spontaneous $CP$ violation as a solution to the strong $CP$ problem in left-right symmetric theories. The discrete $CP$ symmetry is broken by a complex vacuum expectation value of a right-handed Higgs doublet. Heavy vectorlike down-type quarks mix with the Standard Model quarks introducing the known $CP$ violation—realizing a variant of the Nelson-Barr mechanism. A nonvanishing QCD vacuum angle is generated at loop level. The implementation in the ultraviolet complete theory of trinification at low scales is discussed. We further comment on the phenomenology and future testability of the model.