Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

TL;DR

This paper details the four-loop calculation of anomalous dimensions in N=6 superconformal Chern-Simons theories, including wrapping corrections and Feynman diagram analysis, advancing understanding of quantum corrections in these models.

Contribution

It provides a comprehensive four-loop computation of anomalous dimensions and wrapping corrections, with explicit Feynman diagrams and integrals for the first time in this context.

Findings

Explicit four-loop correction to the magnon dispersion relation

Demonstration of cancellation of double poles in renormalization

Detailed Feynman diagram and integral calculations

Abstract

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.