On the current of chiral fermions of higher rank. (Q1609432)

This paper continues previous papers of the author [\textit{M. Schork}, J. Math. Phys. 41, 2443--2459 (2000; Zbl 0974.32012); J. Math. Phys. 42, 4563--4569 (2001; Zbl 1012.81046)] where \(bc\)-systems of higher rank were introduced. An important basic fact is the identification of the determinants of correlation functions with the sections of certain pullbacks of generalized theta bundles. In this paper the 1-point functions of nonabelian currents \(J_{\bigtriangleup\otimes\chi}\) associated to a system of chiral fermions of higher rank are discussed. In particular the expressions for the \(U(1)\)-currents in therms of the theta function are generalized, and their connections to the \(bc\)-systems is found, as well as the relation to the WZW models by means of the Lie algebra \(su(N,\mathbb{C})\) introduced into the local expressions.