PUB - Publikationen an der Universität Bielefeld

We prove a Mahoux-Mehta--type theorem for finite-volume partition functionsof SU(N_c\geq 3) gauge theories coupled to fermions in the fundamentalrepresentation. The large-volume limit is taken with the constraint V <<1/m_{\pi}^4. The theorem allows one to express any k-point correlation functionof the microscopic Dirac operator spectrum entirely in terms of the 2-pointfunction. The sum over topological charges of the gauge fields can beexplicitly performed for these k-point correlation functions. A connection toan integrable KP hierarchy, for which the finite-volume partition function is a$\tau$-function, is pointed out. Relations between the effective partitionfunctions for these theories in 3 and 4 dimensions are derived. We also computeanalytically, and entirely from finite-volume partition functions, themicroscopic spectral density of the Dirac operator in SU(N_c) gauge theoriescoupled to quenched fermions in the adjoint representation. The resultcoincides exactly with earlier results based on Random Matrix Theory.