Thèse Aspects des Dualités Fort-Faible H/F - Doctorat.Gouv.Fr

Établissement : Institut Polytechnique de Paris École polytechnique École doctorale : Ecole Doctorale de l'Institut Polytechnique de Paris Laboratoire de recherche : Centre de Physique Théorique Direction de la thèse : Dario BENEDETTI ORCID 0000000160967641 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-04-30T23:59:59 Studying quantum field theory in a strongly coupled regime remains one of the great challenges of theoretical physics, and it is a compelling motivation for the development of new methods and ideas.
Occasionally, a strongly interacting QFT can be given a completely different description in which it results to be weakly coupled, thus opening the way to computing quantities of interest by means of perturbative methods. In such case we refer to the two descriptions as forming a strong-weak duality.

Dualities can be exact or approximate, in particular, they might be valid only in the infrared limit, in which case we talk about IR dualities. The latter can be very useful in the construction of conformal field theories that arise as nontrivial IR fixed points of a renormalization group flow. If the fixed point in description A is at finite coupling, perturbation theory might be unreliable. On the other hand, if in description B the fixed point is at small coupling, we gain perturbative control over the computation of observables that would require nonperturbative methods in description A.On the other hand, the majority of strong-weak dualities are only conjectural: proving the existence of a (exact or approximate) map between the two description is in general very hard. Therefore, the duality is usually based on symmetry arguments, formal manipulations, and matching of results.
However, for at least one of the two dual descriptions of the theory, matching observables requires computations in a strongly coupled regime, thus bringing back the need for nonperturbative methods.

This situation leads to a practical setting for a theoretical test of methods and conjectures: we can develop and refine nonperturbative methods in order to corroborate the conjectured duality and at the same time use this endeavor as an opportunity to compare different methods and test their power.

The goal of this doctoral project is to tackle such nonperturbative challenge in specific examples of strong-weak dualities, and by different nonperturbative methods.

As working examples, we will work on either recently proposed dualities, or some older ones which are commonly believed to hold but for which either there is no proof or some doubts have been recently cast. An example of the latter case is the duality in dimensions 2
Nonperturbative methods that might be considered include the functional renormalization group,
the fuzzy sphere method, 1/N expansions, and lattice approaches.
Model and method will be adapted to the candidate's interests and inclinations, as well as to contingent developments in the scientific community. Le projet de thèse se situe dans le contexte de la théorie des champs statistiques, et il mélange les méthodes du groupe de renormalisation, de les théories conformes, et de la physique statistique.

Le candidat doit être en train d'achever un M2 en physique théorique. En particulier, le projet nécessite une bonne connaissance de la théorie quantique des champs, de la physique statistique et des méthodes mathématiques.
La maîtrise de l'anglais est indispensable.