Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories

TL;DR

This paper performs a detailed two-loop perturbative calculation of circular 1/2 BPS Wilson loops in ABJ(M) theories, confirming agreement with exact results and analyzing fermionic contributions and evanescent terms.

Contribution

It provides the first complete two-loop perturbative evaluation of 1/2 BPS Wilson loops in ABJ(M) theories, including fermionic couplings and regularization details.

Findings

Perfect agreement with matrix model results at zero framing.

Fermionic contributions are crucial for localization consistency.

Evanescent terms are identified and discussed in relation to Ward identities.

Abstract

We present a complete two-loop analysis of the quantum expectation value for circular BPS Wilson loops in ABJ(M) theories. We examine in details the 1/2 BPS case, that requires non-trivial fermionic couplings with the contour, finding perfect agreement with the exact matrix model answer at zero framing. The result is obtained through a careful application of DRED regularization scheme, combined with a judicious rearrangement of the relevant perturbative contributions that reduces the computation to simple integrals. We carefully analyze the contribution of fermions that is crucial for the consistency with the localization procedure and point out the arising of pivotal evanescent terms, discussing their meaning in relation to Ward identities.