Four loop renormalization of phi^3 theory in six dimensions

TL;DR

This paper performs a four-loop renormalization of six-dimensional phi^3 theory, deriving critical exponents relevant to statistical physics models and extending the analysis to O(N) symmetric theories with comprehensive operator mixing calculations.

Contribution

It provides the first four-loop renormalization of six-dimensional phi^3 theory and computes critical exponents, including operator mixing, with applications to statistical physics and conformal field theories.

Findings

Four-loop beta-function and anomalous dimensions computed.

Critical exponents estimated in 3, 4, and 5 dimensions.

Mass operator mixing matrix eigenvalues agree with large N expansion.

Abstract

We renormalize six dimensional phi^3 theory in the modified minimal subtraction (MSbar) scheme at four loops. From the resulting beta-function, anomalous dimension and mass anomalous dimension we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two dimensional conformal field theory we obtain estimates for exponents in dimensions 3, 4 and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an O(N) symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this O(N) analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigen-exponents are in agreement with the mass exponents computed at O(1/N^2) in the non-perturbative large N expansion.