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000619415 245__ $$a$\mathcal{SW}$-algebras and strings with torsion
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000619415 500__ $$a46 pages plus appendices, 1 figure, 6 tables
000619415 520__ $$aWe explore the connection between super $\mathcal{W}$-algebras ($\mathcal{SW}$-algebras) and $\mathrm{G}$-structures with torsion. The former are realised as symmetry algebras of strings with $\mathcal{N}=(1,0)$ supersymmetry on the worldsheet, while the latter are associated with generic string backgrounds with non-trivial Neveu-Schwarz flux $H$. In particular, we focus on manifolds featuring $\mathrm{Spin}(7)$, $\mathrm{G}_2$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$-structures. We compare the full quantum algebras with their classical limits, obtained by studying the commutators of superconformal and $\mathcal{W}$-symmetry transformations, which preserve the action of the $(1,0)$ non-linear $\sigma$-model. We show that, at first order in the string length scale $\ell_s$, the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.
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000619415 7001_ $$0P:(DE-H253)PIP1103734$$aGaldeano, Mateo$$b1$$eCorresponding author
000619415 7001_ $$0P:(DE-H253)PIP1092973$$aMarchetto, Enrico$$b2$$udesy
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