Noncritical strings and W-algebras

Abstract

Singularities of Spin(7) manifolds are considered in the worldsheet approach, and it is argued that the internal CFT describing a singular spin(7) has an enhanced $\mathcal{S}\mathcal{W}(\frac{3}{2},\frac{3}{2},2)$ algebra tensored with $\mathcal{N}=1$ linear dilaton CFT, much like singular Calabi-Yau CFTs have a $\mathcal{N}=2$ linear dilaton tensored with a suitable $\mathcal{N}=2$ SCFT. Upon adding fundamental strings, these vacua are related to $Ad{S}_3$ vacua with $\mathcal{N}=1$ supersymmetry, completing the worldsheet classification of $Ad{S}_3$ vacua with NS flux.