Calculation of critical index η of the φ3-theory in four-loop approximation by the conformal bootstrap technique

Abstract

The method of calculation of [Formula: see text]-expansion in model of scalar field with [Formula: see text]-interaction based on conformal bootstrap equations is proposed. This technique is based on self-consistent skeleton equations involving full propagator and full triple vertex. Analytical computations of the Fisher’s index [Formula: see text] are performed in four-loop approximation. The three-loop result coincides with one obtained previously by the renormalization group equations technique based on calculation of a larger number of Feynman diagrams. The four-loop result agrees with its numerical value obtained by other authors.