Mcd. Barrozo et Lv. Belvedere, SUPERSYMMETRIC LIOUVILLE THEORY - A STATISTICAL-MECHANICAL APPROACH, Physical review. D. Particles and fields, 53(4), 1996, pp. 2037-2044
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.