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To establish that the QCD topological angle θ must be zero on non-time-orientable spacetimes with Pin⁺ structure.

May 29, 2026Open Access

Topological Constraint on the QCD Vacuum Angle from Pin+ Structure on Non-Time-Orientable Spacetimes

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To establish that the QCD topological angle θ must be zero on non-time-orientable spacetimes with Pin⁺ structure.
Analyzed properties of the first Stiefel-Whitney class and Pin⁺ structures.
Examined the behavior of the QCD θ-term under orientation reversal.
Identified the implications of Pin⁺ manifold characteristics on the stability of θ.
Demonstrated that θ = 0 or θ = π describes identical physics; θ = π is excluded.
Established a single stable vacuum at θ = 0, based on non-consistent vacuum properties of θ = π.
Showed that the finding can be validated through observable consequences in cosmic microwave background polarization.

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We prove that the QCD topological angle is zero in non-time-orientable spacetimes, implying a solution to the strong CP problem.

Fangyuan Hao (2026) studied this question.

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