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 eige nvalues in terms of finite-volume partition functions. This is done fo r both chiral symplectic and chiral unitary random matrix ensembles, w hich correspond to SU(N-c greater than or equal to 3) gauge theories w ith N-f fermions in the adjoint and fundamental representations, respe ctively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding fi nite-volume partition functions. (C) 1998 Elsevier Science B.V. All ri ghts reserved.