Nichtstörungstheoretische Näherungsverfahren für die Operatorproduktentwicklung mit Hilfe der Funktionalen Renormierungsgruppe

• Antragsteller: Dr. Carlo Pagani
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2018 bis 2020
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 416523172

Zusammenfassung der Projektergebnisse

In this project we proposed and tested for the first time a non-perturbative approximation scheme for the operator product expansion coefficients within the functional renormalization group (FRG) framework. The proposed approach has been tested in statistical models such as the O (N ) model in three dimensions. Remarkably, the proposed framework proved to be very versatile and was successfully tested in several corners of the theory, including the large N limit and perturbation theory, and across different space dimensions 2 ≤ d ≤ 4. On the one hand, we verified that by solving the FRG equations perturbatively one recovers the results known from the -expansion. On the other hand, by solving the FRG equations numerically the accuracy of the results greatly improves and is typically between 1% and 3% away from the best results coming from the conformal bootstrap. Remarkably, the investigated methods do not crucially rely neither on conformal symmetry nor on unitarity.

Projektbezogene Publikationen (Auswahl)

• “Operator product expansion coefficients in the exact renormalization group formalism”, Phys. Rev. D 101 (2020) 10
  C. Pagani and H. Sonoda
  
• “Operator product expansion coefficients from the nonperturbative functional renormalization group”. Phys. Rev. D 105, 065020 (2022)
  F. Rose, C. Pagani and N. Dupuis