  We use supersymmetric (SUSY) methods to study the delocalization transition
at zero energy in a one-dimensional tight-binding model of spinless fermions
with particle-hole symmetric disorder. Like the McCoy-Wu random
transverse-field Ising model to which it is related, the fermionic problem
displays two different correlation lengths for typical and mean correlations.
Using the SUSY technique, mean correlators are obtained as quantum mechanical
expectation values for an U(2|1,1) ``superspin''. In the scaling limit, this
quantum mechanics is closely related to a 0+1-dimensional Liouville theory,
allowing an interpretation of the results in terms of simple properties of the
zero-energy wavefunctions. Our primary results are the exact two-parameter
scaling functions for the mean single-particle Green's functions. We also show
how the Liouville quantum mechanics approach can be extended to obtain the full
set of multifractal scaling exponents \tau(q), y(q) at criticality. A thorough
understanding of the unusual features of the present theory may be useful in
applying SUSY to other delocalization transitions.
