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Einstein-Cartan Calculus for Exceptional Geometry

MPS-Authors
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Godazgar,  Hadi
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Godazgar,  Mahdi
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

/persons/resource/persons20713

Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1401.5984.pdf
(Preprint), 295KB

JHEP2014_021.pdf
(Any fulltext), 618KB

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Citation

Godazgar, H., Godazgar, M., & Nicolai, H. (2014). Einstein-Cartan Calculus for Exceptional Geometry. Journal of high energy physics: JHEP, 2014(06): 021. doi:10.1007/JHEP06(2014)021.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0015-7E2B-5
Abstract
In this paper we establish and clarify the link between the recently found E7 generalised geometric structures, which are based on the SU(8) invariant reformulation of D=11 supergravity proposed long ago, and newer results obtained in the framework of recent approaches to generalised geometry, where E7 duality is built in and manifest from the outset. In making this connection, the so-called generalised vielbein postulate plays a key role. We explicitly show how this postulate can be used to define an E7 valued affine connection and an associated covariant derivative, which yields a generalised curvature tensor for the E7 based exceptional geometry. The analysis of the generalised vielbein postulate also provides a natural explanation for the emergence of the embedding tensor from higher dimensions.