$$ \mathcal{SW} $$ -algebras and strings with torsion
Xenia Ossa (Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, U.K.)
; Mateo Galdeano (Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany); Enrico Marchetto (Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, U.K., Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany)
We explore the connection between super $$ \mathcal{W} $$ -algebras ( $$ \mathcal{SW} $$ -algebras) and 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 $\textit{H}$. In particular, we focus on manifolds featuring Spin(7), G , SU(2), and 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 $\textit{σ}$-model. We show that, at first order in the string length scale $\textit{ℓ}$ , the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.
