View source for Knizhnik–Zamolodchikov equation

The '''Knizhnik–Zamolodchikov equation''' is a system of partial differential equations governing the parallel transport of conformal blocks in two-dimensional conformal field theory. Its solutions describe how correlation functions of primary fields vary as insertion points are moved, and the monodromy of these solutions — the transformation undergone when fields are braided around one another — is governed by representations of the [[Braid Group|braid group]]. The KZ equation is not a peripheral tool of string theory; it is the differential realization of the same algebraic structure that underlies [[Topological Quantum Computing|topological quantum computing]].

''The KZ equation reveals that conformal field theory and topological quantum computing are not separate disciplines that happen to share mathematics. They are the same mathematics viewed from different laboratories — one studying the vacuum, the other engineering it.''

[[Category:Mathematics]]
[[Category:Physics]]