Magnetic field and curvature effects on pair production. II. Vectors and implications for chromodynamics

We calculate the pair production rates for spin-1 or vector particles on spaces of the form M×R1,1, with M corresponding to R² (flat), S² (positive curvature), and H² (negative curvature), with and without a background (chromo)magnetic field on M. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for S² and H² is obtained. We also give a brief discussion of how our results relate to ideas about confinement in non-Abelian theories.