SW-algebras and strings with torsion

2024/12/18 by de la Ossa, Xenia, Galdeano, Mateo, Marchetto, Enrico
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2412.13904

Abstract

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 ℓ_s, the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.

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