nLab
current algebra

Idea

A current algebra of a Lie algebra $𝔤$ is a vertex operator algebra describing (one chiral piece of) a string propagating on a Lie group corresponding to $𝔤$.

This appears in the WZW-model 2d sigma-model CFT on $G$.

References

• Sam Treiman, Roman Jackiw, David Gross, Lectures on current algebra and its applications , Princeton University Press. (1972)

• Steven Weinberg, Current Algebra and Gauge Theories. I Phys. Rev. D 8, 605–625 (1973)

• Herbert Pietschmann, On the Early History of Current Algebra (arXiv:1101.2748)