nLab chiral algebra




The syntagm chiral algebra has two meanings: one in physics and a related but more specific one after the work of Beilinson-Drinfeld. In QFT the chiral operator has two classes of eigenmodes left-handed and right-handed; they give rise to left and right chiral fields. CFT in 2d, in particular has two chiral parts expressed via holomorphic and antiholomorphic functions in OPEs.

Beilinson and Drinfel'd were unhappy with non-illuminating definition of vertex operator algebra and invented a mathematical definition of version of chiral conformal field theory on an algebraic curve, under the name chiral algebra; their manuscript has being circulating from around 1995 as a long preprint and being more recently published by Amer. Math. Soc.


The standard textbook is

An “example-driven digest” with applications in string theory is

Generalization to higher algebra is discussed in

Other references

Last revised on December 1, 2020 at 06:32:42. See the history of this page for a list of all contributions to it.