$$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ subsymmetry in G2, Spin(7) and $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ 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 G2 or Spin(7) respectively. We show that these are more than mere analogies. We exhibit an underlying symmetry $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ SW 3 2 2 making a bridge between the latter cases and K3 target spaces. Reviewing unitary representations of $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ SW 3 2 2 leads us to speculate on further roles of this algebra in string theory compactifications and on the existence of topologically twisted versions of $$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ SW 3 2 2 theories.