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arXiv · 1912.11036

Generalised Cosets

Saskia Demulder·Falk Hassler·Giacomo Piccinini·Daniel C. Thompson
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Abstract

Recent work has shown that two-dimensional non-linear $\sigma$-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 $M=\widetilde{G} \backslash D / H$. Mirroring conventional coset geometries, we show that on $M$ one can construct a generalised frame field and a $H$-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 $M$. An important feature is that $M$ 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.

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Saskia Demulder, Falk Hassler, Giacomo Piccinini, Daniel C. Thompson. 2019-12-23. Generalised Cosets. https://arxiv.org/abs/1912.11036

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