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Theses

Renormalisation perturbative et T-dualite - Nouvelles metriques d'Einstein et super-espace harmonique

Abstract : In the first part of the thesis, we adress ourselves the question of the quantum equivalence of non abelian T-dualised sigma-models. We prove that the one-loop renormalisability of initial sigma-models does imply the one-loop renormalisability of their dualised partner, and that they share the same beta functions. This is done for any principal sigma-models defined on a group manifold (G_L X G_R)/G_D with arbitrary breaking of G_R, and for the large class of four dimensional non-homogeneous metrics with an isometry group SU(2) X U(1). For the simple example of the T-dualised SU(2) sigma-model, which has been claimed to be non-renormalisable at the two-loop order, we prove that it is - at least up to this order - still possible to define a correct quantum theory by modifying, at the \hbar order, its target space metric in a finite manner. In the second part, we construct, using harmonic superspace and the quaternionic quotient approach, an explicit quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses U(1) X U(1) isometry and contains as special cases the quaternionic-Kähler extensions of the Taub-NUT and Eguchi-Hanson metrics. It exhibits an extra one-parameter freedom which disappears in the hyper-Kähler limit.
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https://tel.archives-ouvertes.fr/tel-00002166
Contributor : Pierre-Yves Casteill <>
Submitted on : Tuesday, December 17, 2002 - 5:13:01 PM
Last modification on : Wednesday, December 9, 2020 - 3:09:21 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:42:01 PM

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  • HAL Id : tel-00002166, version 1

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Pierre-Yves Casteill. Renormalisation perturbative et T-dualite - Nouvelles metriques d'Einstein et super-espace harmonique. Physique mathématique [math-ph]. Université Paris-Diderot - Paris VII, 2002. Français. ⟨tel-00002166⟩

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