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In the last decade, it was shown that the Liouville field theory is an effective theory of Dirac fermions in the random gauge potential (FRGP). We show that the Dirac wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the quasiclassical approximation of the Liouville theory, our model predicts that the localization length ξ scales with the energy E as $$ \xi \sim E^{{{ - b^2 } \mathord{\left/ {\vphantom {{ - b^2 } {(1 + b^2 )^2 }}} \right. \kern-\nulldelimiterspace} {(1 + b^2 )^2 }}} $$, where b is the strength of the disorder. The self-duality of the theory under the transformation b → 1/ b is discussed. We also calculate the distribution functions of t0 =| ψ0( x)|2, (i.e. p( t0); ψ0( x) is the ground state wave function), which behaves as the log-normal distribution function. It is also shown that in small t0, p( t0) behaves as a chi-square distribution. [ABSTRACT FROM AUTHOR]