Ricci flow, Courant algebroids, and renormalization of Poisson-Lie T-duality

DOI10.1007/s11005-017-0968-5zbMath1378.53095arXiv1610.09004OpenAlexW2545492900MaRDI QIDQ2410937

Fridrich Valach, Pavol Ševera

Publication date: 20 October 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09004

zbMATH Keywords

T-dualityrenormalization group flowRicci flowDirac structuresCourant algebroidsgeneralized complex structuresgeneralized Ricci tensorgeneralized metric, Severa 3-form, Poisson-Lie T-duality

Mathematics Subject Classification ID

Renormalization group methods applied to problems in quantum field theory (81T17) Generalized geometries (à la Hitchin) (53D18)

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Cites Work

• Generalized Kähler geometry
• Torsion-free generalized connections and heterotic supergravity
• Generalized geometry, \(T\)-duality, and renormalization group flow
• Renormalization of Lorentz non-invariant actions and manifest T-duality
• Poisson-Lie T-duality and Courant algebroids
• Manin triples for Lie bialgebroids
• Poisson-Lie \(T\)-duality and loop groups of Drinfeld doubles.
• Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
• Branes on Poisson varieties
• Generalized complex geometry and T-duality
• Courant Algebroids and Poisson Geometry