Resolution of the Strong CP Problem: Why Theta Is Zero on a Discrete Spacetime

The strong CP problem asks why the QCD vacuum angle theta is less than ten to the minus ten when it could naturally be any value up to two pi. For nearly fifty years, the leading solution has been the axion—a hypothetical particle that has never been detected despite decades of dedicated searches.

This paper presents a resolution that requires no new particles. On a fundamentally discrete spacetime with minimum spacing at the Planck scale, the topological charge that makes theta physical in the continuum simply does not exist. Gauge fields on a simplicial lattice are homotopically trivial—any configuration can be continuously deformed to the identity. The theta term, which couples to the topological charge in the continuum, contributes nothing to physical observables in the discrete theory.

The observed experimental bound on theta reflects the exact vanishing of the parameter in the fundamental theory. Tiny apparent violations arise only as artifacts of the continuum approximation and are far below experimental sensitivity. No fine-tuning is required because theta is not a free parameter—it is identically zero by the topology of discrete spacetime.

The same discrete structure that resolves the cosmological constant problem, avoids black hole singularities, and determines the dimensionality of space also sets the strong CP angle to zero. These problems, long considered separate puzzles, share a common origin. No axion. No new symmetries. No fine-tuning. Just the geometry of spacetime at the Planck scale.