Extended degrees of freedom in QFT

Description du projet

Une approche non perturbative pour l’étude des systèmes quantiques à forte interaction

La théorie quantique des champs (TQC) est un pilier de la physique moderne; elle décrit les interactions entre les particules et les systèmes de matière condensée à travers un cadre théorique unifié. Elle est à la base du modèle standard en physique des particules et explique des phénomènes collectifs tels que la supraconductivité dans la matière condensée. Si la TQC décrit efficacement les systèmes à faible interaction, elle peine à rendre compte des phénomènes à forte couplage, tels que les transitions de phase et les interactions nucléaires. Le projet EXTENDED, financé par le CER, portera sur les objets étendus en TQC. On estime que ces objets détiennent la clé permettant de mettre au point un cadre non perturbatif, indispensable pour décrire avec précision des interactions complexes. S’appuyant sur les avancées récentes en matière de méthodes algébriques et géométriques, le projet de recherche proposé vise à mettre au jour de nouveaux principes régissant les systèmes à forte interaction et à développer des outils mathématiques permettant de décrire leurs degrés de liberté étendus.

Objectif

Quantum field theory (QFT) is the formalism that underlies modern particle and condensed matter physics. Standard perturbative methods in QFT have been extraordinarily successful in explaining physical phenomena involving weakly-interacting quantum fields. On the other hand many fundamental phenomena, including phase transitions and nuclear interactions, are described by strongly coupled QFTs for which perturbative techniques are insufficient and a rigorous, predictive theoretical formulation is lacking. Heuristic arguments indicate that a full non-perturbative formulation of QFT must include extended degrees of freedom (a prototypical example being the flux tubes that bind quarks inside the nucleus).

My proposal describes a novel approach for studying extended objects in a wide range of QFTs, based on two recent conceptual breakthroughs: first, my research on a special class of theories (the six-dimensional SCFTs) has brought to light a rich algebraic structure that captures the properties of its stringlike excitations; and second, new developments in mathematics and physics point to the existence of a vast generalization of this structure, which is perfectly suited to describe the extended objects of a much wider range of QFTs.

This program is organized along three directions: analyze the families of QFTs that can be studied by string-theoretic and geometric methods, and gradually uncover the algebraic structures that describe their extended degrees of freedom; exploit these algebraic structures to obtain novel principles that govern the dynamics of strongly-interacting QFTs; and determine the new mathematical structures that arise from the combination of the geometric and algebraic description of the extended objects.

An ERC starting grant will allow me to undertake this ambitious project whose pursuit will lead to a much deeper understanding of extended degrees of freedom, or their role in QFT, and of the mathematical structures that describe them.