The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory

Details The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory

1995-12-17

arxiv.org/abs/hep-th/9512122v1

J.Math.Phys. 37 (1996) 3704-3712

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, uses phyzzx

Scientific paper

10.1063/1.531596

From the time-independent current $\tcj(\bar y,\bar k)$ in the quantum self-dual Yang-Mills (SDYM) theory, we construct new group-valued quantum fields $\tilde U(\bar y,\bar k)$ and $\bar U^{-1}(\bar y,\bar k)$ which satisfy a set of exchange algebras such that fields of $\tcj(\bar y,\bar k)\sim\tilde U(\bar y,\bar k)~\partial\bar y~\tilde U^{-1}(\bar y,\bar k)$ satisfy the original time-independent current algebras. For the correlation functions of the products of the $\tilde U(\bar y,\bar k)$ and $\tilde U^{-1}(\bar y,\bar k)$ fields defined in the invariant state constructed through the current $\tcj(\bar y,\bar k)$ we can derive the Knizhnik-Zamolodchikov (K-Z) equations with an additional spatial dependence on $\bar k$. From the $\tilde U(\bar y,\bar k)$ and $\tilde U^{-1}(\bar y,\bar k)$ fields we construct the quantum-group generators --- local, global, and semi-local --- and their algebraic relations. For the correlation functions of the products of the $\tilde U$ and $\tilde U^{-1}$ fields defined in the invariant state constructed through the semi-local quantum-group generators we obtain the quantum-group difference equations. We give the explicit solution to the two point function.

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