Weyl doubling
Abstract We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Wey...
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doaj-6947e7856efc4318944f6ca43044da8f2020-11-25T03:01:41ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020913010.1007/JHEP09(2020)127Weyl doublingRashid Alawadhi0David S. Berman1Bill Spence2Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of LondonCentre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of LondonCentre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of LondonAbstract We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.http://link.springer.com/article/10.1007/JHEP09(2020)127Classical Theories of GravityGauge-gravity correspondence |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rashid Alawadhi David S. Berman Bill Spence |
spellingShingle |
Rashid Alawadhi David S. Berman Bill Spence Weyl doubling Journal of High Energy Physics Classical Theories of Gravity Gauge-gravity correspondence |
author_facet |
Rashid Alawadhi David S. Berman Bill Spence |
author_sort |
Rashid Alawadhi |
title |
Weyl doubling |
title_short |
Weyl doubling |
title_full |
Weyl doubling |
title_fullStr |
Weyl doubling |
title_full_unstemmed |
Weyl doubling |
title_sort |
weyl doubling |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-09-01 |
description |
Abstract We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors. |
topic |
Classical Theories of Gravity Gauge-gravity correspondence |
url |
http://link.springer.com/article/10.1007/JHEP09(2020)127 |
work_keys_str_mv |
AT rashidalawadhi weyldoubling AT davidsberman weyldoubling AT billspence weyldoubling |
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