Extended degrees of freedom in QFT

Descrizione del progetto

Un approccio non perturbativo allo studio di sistemi quantistici fortemente interagenti

La teoria quantistica dei campi (QFT, Quantum Field Theory) è fondamentale per la fisica moderna e descrive le interazioni tra le particelle e i sistemi di materia condensata attraverso un quadro unificato. Inoltre, è alla base del modello standard della fisica delle particelle e spiega fenomeni collettivi come la superconduttività nella materia condensata. Nonostante la QFT descriva efficacemente sistemi debolmente interagenti, è difficile applicarla a fenomeni fortemente accoppiati come le transizioni di fase e le interazioni nucleari. Il progetto EXTENDED, finanziato dal CER, concentrerà l’attenzione sugli oggetti estesi nella QFT. Si ritiene che questi oggetti siano la chiave per sviluppare un quadro di riferimento non perturbativo, necessario per descrivere accuratamente le interazioni complesse. Sulla base di progressi recenti dei metodi algebrici e geometrici, la ricerca si propone di scoprire nuovi principi che regolano i sistemi fortemente interagenti e di sviluppare strumenti matematici per descrivere i loro gradi di libertà estesi.

Obiettivo

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.