The group theory of oxidation
arXiv:hep-th/0210178 · doi:10.1016/S0550-3213(03)00178-0
Abstract
Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. The reverse process, oxidation, is the reconstruction of a higher dimensional gravity theory from a coset sigma model. Using the group G as starting point, the higher dimensional models follow essentially from decomposition into subgroups. All equations of motion and Bianchi identities can be directly reconstructed from the group lattice, Kaluza-Klein modifications and Chern-Simons terms are encoded in the group structure. Manipulations of extended Dynkin diagrams encode matter content, and (string) dualities. The reflection symmetry of the ``magic triangle'' for E_n gravities, and approximate reflection symmetry of the older ``magic triangle'' of supergravities in 4 dimensions, are easily understood in this framework.
50 pages, LaTeX, 3 figures, 5 tables; v2. typo's fixed, references added, clarified derivation of sigma model equation of motion in appendix D; v3. small corrections, more references
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Cited by in corpus (62)
- Very-extended Kac-Moody algebras and their interpretation at low levels
- Spacelike Singularities and Hidden Symmetries of Gravity
- Generating Geodesic Flows and Supergravity Solutions
- E_11: Sign of the times
- Dimensionally reduced gravity theories are asymptotically safe
- Magic Supergravities, N= 8 and Black Hole Composites
- Kac-Moody Spectrum of (Half-)Maximal Supergravities
- The group theory of oxidation II: Cosets of non-split groups
- Loops in exceptional field theory
- Generalised diffeomorphisms for E
- Hyperbolic billiards of pure D=4 supergravities
- Hidden Symmetries and Dirac Fermions
- Cosmological backgrounds of superstring theory and Solvable Algebras: Oxidation and Branes
- Real Borcherds Superalgebras and M-theory
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- Super-Ehlers in Any Dimension
- Cosmological billiards and oxidation
- G+++ and Brane Solutions
- Tits-Satake projections of homogeneous special geometries
- U-Duality and the Compactified Gauss-Bonnet Term
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- Exceptional Reductions
- Dualisation of the Symmetric Space Sigma Model with Couplings
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- Arithmetic and Hyperbolic Structures in String Theory
- Real forms of extended Kac-Moody symmetries and higher spin gauge theories
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- Kac-Moody Algebras in M-theory
- Oxidation = group theory
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- Symmetric Space Sigma-model Dynamics: Internal Metric Formalism
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- Dualisation of the D=9 Matter Coupled Supergravity
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- The many facets of exceptional field theory
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- OP2 bundles in M-theory
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- Algebraic Integration of Sigma Model Field Equations
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- Exotic Aspects of Extended Field Theories
- Decoupling structure of the principal sigma model-Maxwell interactions