SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs

Abstract

Spectral flow, spacetime supersymmetry, topological twists, chiral primaries related to marginal deformations, mirror symmetry: these are important consequences of the worldsheet 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) making a bridge between the latter cases and K3 target spaces. Reviewing unitary representations of 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 SW(3/2,2) theories.

arXiv comment36 pages, 5 figures

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Cited by in corpus (2)

• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion