Separability in consistent truncations
Abstract
The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying “round metric,” enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, Sn, for n = 2, …, 7, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, wemore »
- Authors:
-
[2];
- Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
- Katholieke Univ. Leuven, Heverlee (Belgium). Instituut voor Theoretische Fysica
- Univ. of Southern California, Los Angeles, CA (United States). Dept. of Physics and Astronomy; Univ. Paris-Saclay, Gif-sur-Yvette (France). Alternative Energies and Atomic Energy Commission (CEA). Centre National de la Recherche Scientifique (CNRS). Institut de Physique Théorique; Univ. of Southern California, Los Angeles, CA (United States). Dept. of Mathematics
- Publication Date:
- Research Org.:
- Univ. of Southern California, Los Angeles, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); European Research Council (ERC)
- OSTI Identifier:
- 1851517
- Grant/Contract Number:
- SC0011687; 787320
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Physics; Space-time symmetries; Supergravity models
Citation Formats
Pilch, Krzysztof, Walker, Robert, and Warner, Nicholas P. Separability in consistent truncations. United States: N. p., 2021.
Web. doi:10.1007/jhep07(2021)008.
Pilch, Krzysztof, Walker, Robert, & Warner, Nicholas P. Separability in consistent truncations. United States. https://doi.org/10.1007/jhep07(2021)008
Pilch, Krzysztof, Walker, Robert, and Warner, Nicholas P. Mon .
"Separability in consistent truncations". United States. https://doi.org/10.1007/jhep07(2021)008. https://www.osti.gov/servlets/purl/1851517.
@article{osti_1851517,
title = {Separability in consistent truncations},
author = {Pilch, Krzysztof and Walker, Robert and Warner, Nicholas P.},
abstractNote = {The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying “round metric,” enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, Sn, for n = 2, …, 7, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, we also make some remarks about separability of the wave equation.},
doi = {10.1007/jhep07(2021)008},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2021,
place = {United States},
year = {Mon Jul 05 00:00:00 EDT 2021},
month = {Mon Jul 05 00:00:00 EDT 2021}
}
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