SUPERSYMMETRIC LIOUVILLE THEORY - A STATISTICAL-MECHANICAL APPROACH

The statistical mechanical system associated with the two-dimensional supersymmetric Liouville theory is obtained through an infrared-finite perturbation expansion. Considering the system confined in a finite v olume and in the presence of a uniform neutralizing background, we sho w that the grand-partition function of this system describes a one-com ponent gas, in which the Boltzmann factor is weighted by an integratio n over the Grassmann variables. This weight function introduces the di mensional reduction phenomenon. After performing the thermodynamic lim it, the resulting supersymmetric quantum theory is translationally inv ariant.