nLab
chiral algebra

Contents

Idea

The syntagm chiral algebra has two meanings: one in physics and a related but more specific one after the work fo 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.

References

The standard textbook is

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

Generalization to higher algebra is discussed in

Other references

Revised on August 17, 2011 22:30:41 by Zoran Škoda (161.53.130.104)