Abstract
We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.
Highlights
Wilson loops (WLs) play an ubiquitous role in gauge theories, both at perturbative and non-perturbative level
We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections
We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit
Summary
Wilson loops (WLs) play an ubiquitous role in gauge theories, both at perturbative and non-perturbative level. The additional couplings between the contour and the fermions appearing in the superconnection may affect the standard analysis presented there Despite of these potential technical issues, we expect the trace of the Wilson line in ABJM to respect the usual exponentiation process, so that. With respect to the winding number n, upon proper identification of the latitude and winding parameters Such a trick was proposed in [34] in the case of the Bremsstrahlung function associated to a cusp constructed with two locally 1/6-BPS rays in ABJM theory. The Bremsstrahlung function associated to a 1/2-BPS cusped WL is given in terms of the expectation value of the 1/6-BPS circular WL, well-known from localization [8, 36]. In this paper we put the conjecture on much firmer grounds, by providing an explicit check of it up to three loop order in perturbation theory, including the sub-leading corrections in N , which first appear at this order
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