Strong-$CP$ with and without gravity

Understand

Conventionally, the strong-$CP$ problem is assumed to be a naturalness puzzle, with the axion solution sometimes viewed as an ad hoc fix.

• Gravity is either ignored or taken as a threat for the global Peccei-Quinn symmetry.
• We explain that the situation is fundamentally different.
• In gravity, axion is a matter of consistency imposed by the $S$-matrix: Each gauge sector must include axion with exact relaxation of the corresponding $\bar{\theta}$.