Adiabatic dilations and essential Regge spectrum

Abstract

Adiabatic perturbation theory works for non-conserved dilation operators. At each effective coupling, all renormalization group functions are dilation eigenvalues of a “tangent” field theory, which preserves scale invariance instead of translation invariance. The adiabatic expansion reconstructs the true field theory from this tangent bundle. For complex angular momentum, the short and long distance expansions mix indecomposably at certain turning points. By connecting the UV and IR limits across them, the adiabatic method determines Regge intercepts from integrals over the renormalization group. Fixed Regge cuts or accumulations of poles are insensitive to the IR region.