Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.13904 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We explore the connection between super $\mathcal{W}$-algebras ($\mathcal{SW}$-algebras) and $\mathrm{G}$-structures with torsion. The former are realised as symmetry algebras of strings with $\mathcal{N}=(1,0)$ supersymmetry on the worldsheet, while the latter are associated with generic string backgrounds with non-trivial Neveu-Schwarz flux $H$. In particular, we focus on manifolds featuring $\mathrm{Spin}(7)$, $\mathrm{G}_2$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$-structures. We compare the full quantum algebras with their classical limits, obtained by studying the commutators of superconformal and $\mathcal{W}$-symmetry transformations, which preserve the action of the $(1,0)$ non-linear $σ$-model. We show that, at first order in the string length scale $\ell_s$, the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.