Framing and localization in Chern-Simons theories with matter

Understand

Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme.

• The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise.
• We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory.
• We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour.