Abstract. We prove that QCD in the -regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential μ. To this aim we prove a theorem that relates integrals over fermionic and bosonic variables to super-Hermitian or super-Unitary groups also called superbosonisation. Our findings extend previous results for the equivalence of the partition functions, spectral densities and the quenched two-point densities. We can show that all k-point density correlation functions agree in both theories for an arbitrary number of quark flavours, for either μ = 0 or μ ≠ 0 taking real or imaginary values. This implies the equivalence for all individual k-th eigenvalue distributions which are particularly useful to determine low energy constants from Lattice QCD with chiral fermions.

Key words: Matrix Models; Chiral Lagrangians

E-print number: 0710.0376
Cited: by
Refers: to

Received 13 October 2007, accepted for publication 28 November 2007
Published 12 December 2007