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(Nc≥3) gauge theories with Nf 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.