Analytic expression for the dimension of the space of conformal blocks in the Wess-Zumino-Novikov-Witten model with gauge group \(SU(2)\). (English. Russian original) Zbl 0811.58011

Piunikhin, S. A.

Funct. Anal. Appl. 27, No. 4, 251-256 (1993); translation from Funkts. Anal. Prilozh. 27, No. 4, 32-39 (1993).

An analytic expression for the dimension of the space \(V_ g\) of conformal blocks on a Riemann surface of genus \(g\) with \(N\) external fields is obtained by using the Verlinde formula. The Wess-Zumino- Novikov-Witten (WZNW) model with the gauge group \(\text{SU}(2)\) is considered. In this case, \(V_ g\) is defined as the space of holomorphic sections of some line bundle over the moduli space of flat \(\text{SU}(2)\)-connections on a Riemann surface of genus \(g\). A combinatorial description of the space \(V_ g\) is given. Then, an analytical expression for the dimension of the space \(V_ g\) on the torus with two external fields is determined. Using this expression, the generating function of the dimensions of the spaces \(V_ g\) \((g = 0, 1, \dots)\) is calculated for the WZNW model.

Reviewer: G.Zet (Iaşi)

MSC:

58D15	Manifolds of mappings
81T60	Supersymmetric field theories in quantum mechanics

Keywords:

space of conformal blocks; Verlinde formula; gauge group; generating function

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