RG analysis at higher orders in perturbative QFTs in CMP

TL;DR

This paper computes four-loop beta functions and anomalous dimensions for several chiral models in four dimensions, and extrapolates critical exponents to three dimensions using Padé approximants, advancing perturbative quantum field theory analysis.

Contribution

It provides the first four-loop calculations of beta functions and anomalous dimensions for these models and introduces Padé extrapolation of critical exponents to three dimensions.

Findings

Four-loop beta functions and anomalous dimensions computed.

Padé extrapolation applied to estimate 3D critical exponents.

Results improve understanding of IR fixed points in chiral models.

Abstract

In this contribution we report on the perturbative determination of $\beta$-functions and anomalous dimensions for the chiral Ising, chiral XY and chiral Heisenberg Gross-Neveu-Yukawa model around $D=4$ dimensions at four loops and the first Pad\'e extrapolation of critical exponents at non-trivial, infrared stable fixed points to $D=3$ to this order. This talk is based on Ref. [Zerf:2017zqi].