Scaling laws, renormalization group flow and the continuum limit in noncompact lattice QED
Abstract
We investigate the ultraviolet behavior of noncompact lattice QED with ligth staggered fermions. The main question is whether QED is a nontrivial theory in the continuum limit, and if not, what is its range of validity as a lowenergy theory. Perhaps the limited range of validity could offer an explanation of why the finestructure constant is so small. Noncompact QED undergoes a secondorder chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the CallanSymanzik βfunction in the critical region. No ultraviolet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cutoff theory. We evaluate the maximum value of the cutoff as a function of the renormalized charge. Next, we compute the masses of fermionantifermion composite states. The scaling behavior of these masses is well described by an effective action with meanfield critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is noninteracting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for small renormalized charges.
 Publication:

Nuclear Physics B
 Pub Date:
 March 1992
 DOI:
 10.1016/05503213(92)906936
 Bibcode:
 1992NuPhB.371..713G