Zero modes, beta functions and IR/UV interplay in higher-loop QED

We analyze the relation between the short-distance behavior of quantum fieldtheory and the strong-field limit of the background field formalism, for QEDeffective Lagrangians in self-dual backgrounds, at both one and two loop. Theself-duality of the background leads to zero modes in the case of spinor QED,and these zero modes must be taken into account before comparing theperturbative beta function coefficients and the coefficients of thestrong-field limit of the effective Lagrangian. At one-loop this is familiarfrom instanton physics, but we find that at two-loop the role of the zeromodes, and the interplay between IR and UV effects in the renormalization, isquite different. Our analysis is motivated in part by the remarkable simplicityof the two-loop QED effective Lagrangians for a self-dual constant background,and we also present here a new independent derivation of these two-loopresults.Comment: 15 pages, revtex