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

Abstract

We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2{)}_k)$ for arbitrary level $k$ and representation $j\le k/2$. 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.

20 pages, LaTex. Minor changes

References in corpus (1)

• Correlation Functions of the XXZ model for $\Delta <-1$

Cited by in corpus (5)

• $U_q[\widehat{sl(2|1)}]$ Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level
• Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations
• N-point matrix elements of dynamical vertex operators of the higher spin XXZ model
• Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation
• q-Wakimoto Modules and Integral Formulae of the Quantum Knizhnik-Zamolodchikov Equations