ABJM $\theta$-Bremsstrahlung at four loops and beyond

TL;DR

This paper computes the four-loop weak coupling internal space -Bremsstrahlung function in ABJ(M) theory and proposes an all-order conjecture based on the results, advancing understanding of generalized cusps in supersymmetric gauge theories.

Contribution

It provides the first four-loop calculation of the -Bremsstrahlung function in ABJ(M) theory and introduces a conjecture for its all-order behavior.

Findings

Computed the -Bremsstrahlung function to four loops at weak coupling.

Proposed an all-order conjecture for the -Bremsstrahlung function.

Enhanced understanding of generalized cusps in supersymmetric gauge theories.

Abstract

In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS Wilson line by introducing an angle $\varphi$ in the spacial contour and/or an angle $\theta$ in the internal R-symmetry space. The small angles limits of its anomalous dimension are controlled by corresponding Bremsstrahlung functions. In this note we compute the internal space $\theta$-Bremsstrahlung function to four loops at weak coupling in the planar limit. Based on this result, we propose an all order conjecture for the $\theta$-Bremsstrahlung function.