Universal two-parameter $\mathcal{W}_{\infty}$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots, N)$

Andrew R. Linshaw

Published 2017-10-06Version 1

We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by the weights $2$ and $3$ fields. Subject to some mild constraints, all vertex algebras of type $\mathcal{W}(2,3,\dots, N)$ for some $N$ can be obtained as quotients of this universal algebra.