A Vacuum Accumulation Solution to the Strong CP Problem

TL;DR

The paper reframes the strong CP problem in terms of a four-form field strength F and theta-vacua, proposing a non-axionic solution based on vacuum-accumulation driven by CP-odd 2-branes that source the QCD Chern-Simons form. This attractor dynamics concentrates an infinite number of vacua toward theta = 0 (i.e., F = 0), with the vacua count diverging as theta approaches zero while large-theta vacua remain measure-zero. It predicts potentially light membrane resonances coupled to Standard Model gauge fields that could be produced at colliders, and it implements a dynamical fix against shifts from electroweak CP violation via spontaneous CP breaking with brane-localized suppression. The framework offers a novel, axion-free route to the strong CP problem with distinctive experimental signatures such as brane resonances and possible new short-range forces.

Abstract

We suggest a solution to the strong CP problem in which there are no axions involved. The superselection rule of the θ-vacua is dynamically lifted in such a way that an infinite number of vacua are accumulated within the phenomenologically acceptable range of θ< 10^{-9}, whereas only a measure-zero set of vacua remains outside of this interval. The general prediction is the existence of membranes to which the standard model gauge fields are coupled. These branes may be light enough for being produced at the particle accelerators in form of the resonances with a characteristic membrane spectrum.