Mapping the vacuum structure of gauged maximal supergravities: an application of high performance symbolic algebra
Mapping the vacuum structure of gauged maximal supergravities: an application of high performance symbolic algebra
The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally challenging task due to the occurrence of the exceptional Lie groups $E_6$, $E_7$, $E_8$ in the definition of these potentials. At present, the most promising approach to gain information about nontrivial vacua of these models is to perform a truncation of the potential to submanifolds of the $G/H$ coset manifold of scalars which are invariant under a subgroup of the gauge group and of sufficiently low dimension to make an analytic treatment possible.
New tools are presented which allow a systematic and highly effective study of these potentials up to a previously unreached level of complexity. Explicit forms of new truncations of the potentials of four- and three-dimensional models are given, and for N=16, D=3 supergravities, which are much more rich in structure than their higher-dimensional cousins, a series of new nontrivial vacua is identified and analysed
symbolic algebra, supergravity, databases, optimization, sparse higher rank tensors, spontaneous symmetry breaking, topological field theory
Fischbacher, Thomas
d3282f31-0a6a-4d19-80d0-e3bebc12f67a
May 2003
Fischbacher, Thomas
d3282f31-0a6a-4d19-80d0-e3bebc12f67a
Fischbacher, Thomas
(2003)
Mapping the vacuum structure of gauged maximal supergravities: an application of high performance symbolic algebra.
Humboldt Universitaet zu Berlin, School of Physics, Doctoral Thesis, 140pp.
Record type:
Thesis
(Doctoral)
Abstract
The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally challenging task due to the occurrence of the exceptional Lie groups $E_6$, $E_7$, $E_8$ in the definition of these potentials. At present, the most promising approach to gain information about nontrivial vacua of these models is to perform a truncation of the potential to submanifolds of the $G/H$ coset manifold of scalars which are invariant under a subgroup of the gauge group and of sufficiently low dimension to make an analytic treatment possible.
New tools are presented which allow a systematic and highly effective study of these potentials up to a previously unreached level of complexity. Explicit forms of new truncations of the potentials of four- and three-dimensional models are given, and for N=16, D=3 supergravities, which are much more rich in structure than their higher-dimensional cousins, a series of new nontrivial vacua is identified and analysed
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Published date: May 2003
Additional Information:
This thesis won the Max Planck Society's Otto Hahn Medal
Keywords:
symbolic algebra, supergravity, databases, optimization, sparse higher rank tensors, spontaneous symmetry breaking, topological field theory
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Local EPrints ID: 46366
URI: http://eprints.soton.ac.uk/id/eprint/46366
PURE UUID: d03fdaa2-4933-4bff-9cd0-8dfa13ac596a
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Date deposited: 22 Jun 2007
Last modified: 11 Dec 2021 16:33
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Author:
Thomas Fischbacher
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