On the supersymmetric partition function in QCD-inspired random matrix models

We show that the expression for the supersymmetric partition function of the chiral Unitary Ensemble conjectured recently by Splittorff and Verbaarschot [Phys. Rev. Lett. v. 90, 041601 (2003)] follows from the general expression derived recently by Fyodorov and Strahov [ J. Phys. A: Math.Gen.} {\bf 36}(2003) 3203] .
This is a modified published version, with some updated references. Pis'ma v ZhETF v.77 (2003), 513 [Eng. Transl.: JETP Lett. v.77, to appear]