Disordered Dirac Fermions: the Marriage of Three Different Approaches

We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su(N) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N=2 case. We demonstrate that this menage a trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c=-2 theory of dense polymers. The presence of the c=-2 theory may be seen in all three different treatments of the disorder.