Equivalence of 1-loop RG flows in 4d Chern-Simons and integrable 2d sigma-models

TL;DR

This paper demonstrates that the 1-loop renormalization group flows of 4d Chern-Simons theory with defects are equivalent to those of certain integrable 2d sigma-models, establishing a deep connection between these theories.

Contribution

It provides a proof that 1-loop divergences in 4d Chern-Simons theory match those in integrable 2d sigma-models, using an alternative path integral approach and classical equivalence.

Findings

1-loop divergences localize to 2d defects

Matching of 1-loop RG flows between 4d and 2d theories

Validation of universal formulas for 2d sigma-models

Abstract

We argue for the matching of 1-loop divergences between 4d Chern-Simons theory with Disorder defects and the corresponding integrable 2d sigma-models of non-ultralocal type. Starting from the 4d path integral, we show under general assumptions that the 1-loop divergences localise to the 2d defects. They match the 'universal' formulae developed in [arXiv:2209.05502] for the 1-loop RG flows of integrable 2d sigma-models. Our argument uses an alternate path integral representation for the 1-loop effective action and the known classical equivalence between the 4d and 2d theories.