SW -algebras and strings with torsion

Journal article

We explore the connection between super W-algebras (SW-algebras) and G-structures with torsion. The former are realised as symmetry algebras of strings with 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 Spin(7), G2, SU(2), and SU(3)-structures. We compare the full quantum algebras with their classical limits, obtained by studying the commutators of superconformal and 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 ℓs, the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.

Authors: de la Ossa, X; Galdeano, M; Marchetto, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2025
• Issue: 4
• Article number: 157
• Publication date: 2025-04-18
• Acceptance date: 2025-03-15
• DOI: 10.1007/jhep04(2025)157
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Superstrings and Heterotic Strings; Conformal and W Symmetry; Sigma Models