Generalised cosets

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>Recent work has shown that two-dimensional non-linear <jats:italic>σ</jats:italic>-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to target spaces constructed as double cosets <jats:italic>M</jats:italic> = <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \tilde{G} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>G</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula>\<jats:italic>𝔻</jats:italic>/<jats:italic>H</jats:italic>. Mirroring conventional coset geometries, we show that on <jats:italic>M</jats:italic> one can construct a generalised frame field and a <jats:italic>H</jats:italic> -valued generalised spin connection that together furnish an algebra under the generalised Lie derivative. This results naturally in a generalised covariant derivative with a (covariantly) constant generalised intrinsic torsion, lending itself to the construction of consistent truncations of 10-dimensional supergravity compactified on <jats:italic>M</jats:italic> . An important feature is that <jats:italic>M</jats:italic> can admit distinguished points, around which the generalised tangent bundle should be augmented by localised vector multiplets. We illustrate these ideas with explicit examples of two-dimensional parafermionic theories and NS5-branes on a circle.</jats:p>