Théorique, numérique
In the late 1960s, Wilson and Kadanoff suggested independently that in a quantum field theory the product of two operators in the short distance limit is equivalent to an infinite sum of operators multiplied by functions when inserted in any correlation function. This so-called operator product expansion (OPE) is of fundamental importance in the study of conformal field theories (CFTs) in two and higher dimensions. Along with the knowledge of the operators’ scaling dimensions and spins, the OPE coefficients entirely determine the CFT. Unfortunately, the computation of these coefficients is difficult. One possible tool to that effect is the nonperturbative functional renormalization group (FRG), a versatile method that has been used to study a variety of strongly correlated systems from high-energy physics to condensed matter theory. The FRG has been used to recently extract from the momentum dependence of the correlation functions the leading order OPE coefficients in these models. The goal of the internship is to extend these results and determine high-order OPE coefficients via the FRG. First, the intern will get familiar with the FRG and its momentum-dependence preserving approximation schemes. During the second part of the internship, they will generalize the method developed in [Rose, Pagani, and Dupuis, Phys. Rev. D 105, 065020 (2022)] to determine higher-order OPE coefficients from the study of the RG fixed point equations.