Calculation of critical index $\eta$ of the $\varphi^3$-theory in 4-loop approximation by the conformal bootstrap technique

TL;DR

This paper introduces a conformal bootstrap method to calculate the critical index η in the φ^3-theory at four-loop order, providing analytical results that align with previous numerical and RG findings.

Contribution

It develops a novel conformal bootstrap approach for ε-expansion in φ^3-theory, enabling analytical four-loop calculations of the Fisher's index η.

Findings

Four-loop analytical value of η obtained.

Results agree with previous numerical and RG calculations.

Method offers a new analytical tool for critical index computation.

Abstract

The method of calculation of $\varepsilon$-expansion in model of scalar field with $\varphi^3$-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 $\eta$ 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.