Interpolating bremsstrahlung function in ABJM model

In ABJM theory, enriched RG flows between circular <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>6</a:mn></a:mrow></a:math> BPS bosonic and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math> BPS fermionic Wilson loops have been introduced in L. Castiglioni [L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, .]. These flows are triggered by deformations corresponding to parametric <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>6</e:mn></e:mrow></e:math> BPS fermionic loops. In this paper, we revisit the study of these operators, but instead of circular contours, we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mn>1</g:mn><g:mo>/</g:mo><g:mn>6</g:mn></g:mrow></g:math> BPS fermionic and the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>1</i:mn><i:mo>/</i:mo><i:mn>6</i:mn></i:mrow></i:math> BPS bosonic Wilson lines.