On Sibling and Exceptional W Strings

TL;DR

This paper explores the physical spectrum of various $W$ strings linked to specific Lie algebras, revealing connections with well-known minimal models in conformal field theory, and extends understanding of their algebraic structures.

Contribution

It identifies the spectrum of $W$ strings associated with $B_n$, $D_n$, $E_6$, $E_7$, and $E_8$ algebras and relates them to minimal models, highlighting new algebraic connections.

Findings

Connection between simply-laced $W$ strings and $(h,h+1)$ Virasoro minimal models

Link between $B_n$ $W$ strings and $(2h,2h+2)$ super-Virasoro models

Spectrum characterization for $W$ strings based on various Lie algebras

Abstract

We discuss the physical spectrum for $W$ strings based on the algebras $B_n$, $D_n$, $E_6$, $E_7$ and $E_8$. For a simply-laced $W$ string, we find a connection with the $(h,h+1)$ unitary Virasoro minimal model, where $h$ is the dual Coxeter number of the underlying Lie algebra. For the $W$ string based on $B_n$, we find a connection with the $(2h,2h+2)$ unitary $N=1$ super-Virasoro minimal model.