We show that the Gribov horizon is contained within a certain ellipsoid whose principal axes lie along Fourier coefficients of the connection A(x). This implies the bound on the Fourier transform g(k) of the gluon propagator (more generally, the two-point function of the connection) in D euclidean space-time dimensions, ∫dDk g(k)/k2 < constant. For D = 4, this bound is not compatible with the asymptotic behavior at large momentum predicted by the perturbative renormalization group.
ASJC Scopus subject areas
- Nuclear and High Energy Physics