Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

TL;DR

This paper computes the four-loop spectrum of certain operators in N=6 supersymmetric Chern-Simons theories using superspace techniques, providing new insights into the magnon dispersion relation and its all-loop behavior.

Contribution

It introduces a superspace method to calculate the four-loop spectrum in ABJM and ABJ theories, revealing the fixed transcendentality of the function h^2(λ) and discussing its all-loop interpolation.

Findings

Four-loop contribution to h^2(λ) matches previous component results.

The computed spectrum confirms fixed transcendentality at four loops.

Discussion of potential all-loop functions h^2(λ) bridging weak and strong coupling regimes.

Abstract

Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(\lambda) that interpolates between weak and strong couplings.