SW 3 2 2 $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ subsymmetry in G2, Spin(7) and N $$ \mathcal{N} $$ = 2 CFTs

Abstract

Abstract Spectral flow, spacetime supersymmetry, topological twists, chiral primaries related to marginal deformations, mirror symmetry: these are important consequences of the worldsheet N $$ \mathcal{N} $$ = 2 superconformal symmetry of strings on Calabi-Yau manifolds. To various degrees of certainty, these features were also established when the target is either 7d or 8d with exceptional holonomy G 2 or Spin(7) respectively. We show that these are more than mere analogies. We exhibit an underlying symmetry SW 3 2 2 $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ making a bridge between the latter cases and K3 target spaces. Reviewing unitary representations of SW 3 2 2 $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ leads us to speculate on further roles of this algebra in string theory compactifications and on the existence of topologically twisted versions of SW 3 2 2 $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ theories.

Keywords

• Conformal and W Symmetry
• Conformal Field Models in String Theory