New insights into two-loop running in effective field theories

TL;DR

This paper introduces a novel method to compute two-loop anomalous dimensions in effective field theories by relating 4D theories to their 5D compactified counterparts, avoiding traditional gauge-breaking techniques.

Contribution

It provides a new approach to calculate two-loop anomalous dimensions using IR-UV correspondence in 5D to 4D matching, enabling cross-checks and novel computations in SMEFT and critical phenomena.

Findings

Validated the method by reproducing known results

Computed new two-loop anomalous dimensions in SMEFT to dimension eight

Determined critical exponents in the Abelian Higgs model at large flavors

Abstract

We show that, by viewing a 4D effective-field theory as the infrared (IR) limit of the compactified version in 5D, we can compute two-loop anomalous dimensions without gauge-breaking counter-terms, IR re-arrangement or geometric methods. The ultraviolet (UV) divergences in 4D are read from the IR ones in the matching from 5D to 4D. We use this approach to cross-check recent results in the literature, as well as to compute novel two-loop anomalous dimensions in the SMEFT to dimension eight and certain critical exponents in the charged fixed point of the Abelian Higgs model at large number of flavors.