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Journal of High Energy Physics

, 2019:19 | Cite as

Adjoint orbits, generalised parallelisable spaces and consistent truncations

  • Louise AndersonEmail author
Open Access
Regular Article - Theoretical Physics
  • 12 Downloads

Abstract

The aim of this note is to present some new explicit examples of O(d, d)generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits \( \mathcal{O} \) of some semi-simple Lie group G. Using this construction, an explicit expression for a generalised frame is given in the case when the orbits are regular, but subtleties arise when they become degenerate. In the case of regular orbits, the resulting space is a globally flat fiber bundle over \( \mathcal{O} \) which can be made compact, allowing for a generalised Scherk-Schwartz reduction. This means these spaces should admit consistent supergravity truncations. For degenerate orbits, the procedure hinges on the existence of a suitable metric, allowing for a consistent normalisation of the generalised frame.

Keywords

Differential and Algebraic Geometry Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.The Blackett LaboratoryImperial College LondonLondonUnited Kingdom

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