Strong coupling in the Liouville theory: a heuristic approach

Abstract

The Liouville action F=[ (25−d) 48π ]ʃ[ 1 2 (∇φ) 2+λ e φ] d 2x , with proper-time cutoff ϵ, is considered. It is suggested that for d > 1 (strong coupling) the appropriate control parameter is not λ but μ= λϵ, and that a branched polymer critical point occurs at a strictly positive μ c ( d). For μ< μ c , the term in λ may fail to control infinite nestings of conformal spikes corresponding to branching tubules, of cross section ϵ, in real space. It is conjectured that the spacing between branch points becomes large as d→1 +: if so, an expansion in d−1 might be useful to access the branched polymer fixed point.