Vertex Operators and Matrix Elements of $U_q(su(2)_k)$ via Bosonization

Details Vertex Operators and Matrix Elements of $U_q(su(2)_k)$ via Bosonization Vertex Operators and Matrix Elements of $U_q(su(2)_k)$ via Bosonization

1993-05-25

arxiv.org/abs/hep-th/9305127v2

Int.J.Mod.Phys.A9:4431-4448,1994

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTex. Minor changes

Scientific paper

10.1142/S0217751X9400176X

We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2)_k)$ for arbitrary level $k$ and representation $j\leq k/2$. Both are obtained directly as two solutions of the defining condition of vertex operators - namely that they intertwine $U_q(su(2)_k)$ modules. We construct the screening charge and present a formula for the n-point function. Specializing to $j=1/2$ we construct all VOs and CVOs explicitly. The existence of the CVO allows us to place the calculation of the two-point function on the same footing as $k=1$; that is, it is obtained without screening currents and involves only a single integral from the CVO. This integral is evaluated and the resulting function is shown to obey the q-KZ equation and to reduce simply to both the expected $k=1$ and $q=1$ limits.

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