Hamiltonian Formulation of Open WZW Strings

TL;DR

This paper develops a Hamiltonian framework for open WZW strings, revealing a new non-commutative geometry at the boundary and deriving the quantum operator algebra and conformal field theory equations.

Contribution

It introduces a Hamiltonian approach to open WZW strings, uncovering non-abelian boundary effects and formulating the quantum operator algebra and KZ equations.

Findings

Discovery of a non-commutative boundary geometry.

Derivation of the quantum operator algebra for open WZW strings.

Formulation of the boundary analogue of the Knizhnik-Zamolodchikov equations.

Abstract

Using a Hamiltonian approach, we construct the classical and quantum theory of open WZW strings on a strip. (These are the strings which end on WZW branes.) The development involves non-abelian generalized Dirichlet images in an essential way. At the classical level, we find a new non-commutative geometry in which the equal-time coordinate brackets are non-zero at the world-sheet boundary, and the result is an intrinsically non-abelian effect which vanishes in the abelian limit. Using the classical theory as a guide to the quantum theory, we also find the operator algebra and the analogue of the Knizhnik-Zamolodchikov equations for the the conformal field theory of open WZW strings.