Dimensionally reduced gravity, Hermitian symmetric spaces and the Ashtekar variables

DOI10.1088/0264-9381/17/14/310zbMath1040.83003arXivgr-qc/9911118OpenAlexW2051869212MaRDI QIDQ4457601

Marco Zagermann, Othmar Brodbeck

Publication date: 25 March 2004

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/9911118

zbMATH Keywords

supergravityEinstein equationHermitian symmetric spacesdimensional reductions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Analogues of general relativity in lower dimensions (83C80)

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Flag manifold sigma models. Spin chains and integrable theories ⋮ Integrable deformations of sigma models ⋮ Ultralocal Lax connection for para-complex \(\mathbb{Z}_T\)-cosets ⋮ Flag manifold sigma models and nilpotent orbits ⋮ Quantum flag manifold \(\sigma \)-models \textit{and} Hermitian Ricci flow ⋮ Dimensionally reduced gravity theories are asymptotically safe ⋮ Sigma models as Gross-Neveu models

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