DISORDERED DIRAC FERMIONS - MULTIFRACTALITY TERMINATION AND LOGARITHMIC CONFORMAL FIELD-THEORIES

We reexamine in detail the problem of fermions interacting with a non- Abelian random vector potential. Without resorting to the replica or s upersymmetry approaches, we show that in the limit of infinite disorde r strength the theory possesses an exact solution which takes the form of a logarithmic conformal field theory. We show that the proper trea tment of the locality conditions in the SU(2) theory leads to the term ination of the multifractal spectrum, or in other words to the termina tion of the infinite hierarchies of negative-dimensional operators tha t were thought to occur. Based on arguments of logarithmic degeneracie s, we conjecture that such a termination mechanism should be present f or general SU(N). Moreover, our results lead to the conclusion that th e previous replica solution of this problem yields incorrect results. (C) 1998 Elsevier Science B.V.