Non-perturbative approximation schemes for the operator product expansion via the functional renormalization group

• Applicant: Dr. Carlo Pagani
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 416523172

Final Report Abstract

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.

Publications

• “Operator product expansion coefficients in the exact renormalization group formalism”, Phys. Rev. D 101 (2020) 10
  C. Pagani and H. Sonoda
  (See online at https://doi.org/10.1103/PhysRevD.101.105007)
• “Operator product expansion coefficients from the nonperturbative functional renormalization group”. Phys. Rev. D 105, 065020 (2022)
  F. Rose, C. Pagani and N. Dupuis
  (See online at https://doi.org/10.1103/PhysRevD.105.065020)