We discuss the spontaneous CP violation in Yang-Mills theory in four dimensions with the gauge group SU(N). For this purpose, we investigate Yang-Mills theory on T4 with the gauge group SU(N)/ZN instead. The finite volume correction in this theory strongly suggests that the free energy density has a cusp in the range (0,π) of the θ-angle. This then implies the existence of the same cusp at θ=π in SU(N) theory, indicating the spontaneous CP violation.
