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Des théories quantiques de champ topologiques aux théories de jauge supersymétriques

Abstract : This thesis contains tow parts based on scientific contributions that have led to two series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so called Baulieu-Singer equation. Together with the topological BRST operator, this symmetry gives an off-shell closed subsector of supersymmetry that permits to determine the action uniquely.

The second part proposes a methodology for renormalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of two consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the beta function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory.

After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in twisted superspace.
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Contributor : Guillaume Bossard <>
Submitted on : Friday, November 23, 2007 - 5:18:07 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:43 PM
Long-term archiving on: : Thursday, September 27, 2012 - 10:16:03 AM

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  • HAL Id : tel-00191113, version 1

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Guillaume Bossard. Des théories quantiques de champ topologiques aux théories de jauge supersymétriques. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00191113⟩

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