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Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives
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The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. In many cases of interest there are also covariantly constant one-forms which also give rise to symmetries. These geometries are of interest in the context of heterotic supergravity solutions and the associated reductions are studied from a spacetime point of view via the Killing spinor equations.
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Cited by 2 Pith papers
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$\mathcal{SW}$-algebras and strings with torsion
For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.
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Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.
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