Consistency conditions for finite-volume partition functions

Using relations from random matrix theory, we derive exact expressions for all n-point spectral correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to SU(N-c greater than or equal to 3) gauge theories with N-f fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions. (C) 1998 Elsevier Science B.V. All rights reserved.