Random Dirac Fermions: The su(N) Gauge Potential and Zₙ Twists

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We obtain the disorder averaged (critical) four-point correlation functions for N species of (two-dimensional Euclidean) Dirac fermions subject to a (Gaussian) random su(N) gauge field. The replica approach and the strong disorder approach yield identical results, as one might expect in the light of recent developments in the N=2 case [1]. We establish a connection with `dressed' Zₙ twist fields in the c=-2 logarithmic conformal field theory (LCFT), thereby extending the recent connection to `dressed' Z₂ twists [1,2]. We draw attention to the fact that `dressed' Z₂ twist operators have previously appeared in the description of half flux-quantum quasiholes in the bulk excitations of the Haldane--Rezayi Quantum Hall state [3].