On the current of chiral fermions of higher rank. (English) Zbl 1033.81042
This paper continues previous papers of the author [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.
Reviewer: Rutwig Campoamor-Stursberg (Mulhouse)
MSC:
81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
14H60 | Vector bundles on curves and their moduli |
14K25 | Theta functions and abelian varieties |
22E70 | Applications of Lie groups to the sciences; explicit representations |
14H42 | Theta functions and curves; Schottky problem |
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |