nLab W algebra

Idea

A W algebra is a higher spin extension of the Virasoro algebra. It is an extended symmetry algebra in conformal field theory.

References

An early survey is

• Peter Bouwknegt, Kareljan Schoutens, W symmetry in conformal field theory, Phys. Rep. 223:4 (1993) 183–276 doi

• Peter Bouwknegt, Jim McCarthy, Krzysztof Pilch, The $W_3$ algebra: modules, semi-infinite cohomology, and BV algebras, Lec. Notes in Phys. 42, Springer 1996 (doi:10.1007/978-3-540-68719-1)

• Wikipedia, W-algebra

Relation to Jordan algebra is discussed in

• L. J. Romans, Realisations of classical and quantum $W_3$ symmetry, Nuclear Physics B 352:3 (1991) 829–848 doi

Relation to L-infinity algebras is discussed in

• Ralph Blumenhagen, Michael Fuchs, Matthias Traube, $\mathcal{W}$-Algebras are $L_\infty$-algebras (arXiv:1705.00736)

Relation to brane intersection in M-theory

• Davide Gaiotto, Miroslav Rapčák, Yehao Zhou. Deformed Double Current Algebras, Matrix Extended $W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection (2023). (arXiv:2309.16929).

category: physics, algebra