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Journal of High Energy Physics

, 2015:153 | Cite as

On the exceptional generalised Lie derivative for d ≥ 7

  • J. A. Rosabal
Open Access
Regular Article - Theoretical Physics

Abstract

In this work we revisit the \( {E}_8\times {\mathrm{\mathbb{R}}}^{+} \) generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the \( {E}_7\times {\mathrm{\mathbb{R}}}^{+} \) one. Compared to its \( {E}_d\times {\mathrm{\mathbb{R}}}^{+} \), d ≤ 7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E 8 group, are needed to have a well defined theory. We discuss the implications of the structure of the \( {E}_8\times {\mathrm{\mathbb{R}}}^{+} \) generalised transformation on the construction of the d = 8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.

Keywords

String Duality Flux compactifications M-Theory 

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) 2015

Authors and Affiliations

  1. 1.Departamento de Física, Universidad de Buenos Aires CONICET-UBABuenos AiresArgentina
  2. 2.Institut de Physique Théorique, CEA/ SaclayGif-sur-Yvette CedexFrance

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