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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.13904 |
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| _version_ | 1866909624363384832 |
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| author | de la Ossa, Xenia Galdeano, Mateo Marchetto, Enrico |
| author_facet | de la Ossa, Xenia Galdeano, Mateo Marchetto, Enrico |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathcal{SW}$-algebras and strings with torsion de la Ossa, Xenia Galdeano, Mateo Marchetto, Enrico High Energy Physics - Theory Quantum Algebra 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. |
| title | $\mathcal{SW}$-algebras and strings with torsion |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2412.13904 |