Abstract
We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially extend its recent four-loop computation at weak coupling to include non-planar corrections. We have recently proposed a conjecture relating this object to supersymmetric circular Wilson loops with multiple windings, which can be computed via localization. We find agreement between this proposal and the perturbative computation of the Bremsstrahlung function, including color sub-leading corrections. This supports the conjecture and hints at its validity beyond the planar approximation.
Highlights
In a recent publication [13] we computed the weak coupling four-loop corrections to the θ-Bremsstrahlung function
Comparison with a localization based prediction for the Bremsstrahlung function is attained by first determining an explicit expression for the 1/6-BPS circular Wilson loop, multiply wound around the great circle
In order to check a possible extension to the color sub-leading case, we need an explicit expansion of the multiply wound 1/6-BPS Wilson loop to four loops
Summary
We consider the U(N1)k × U(N2)−k ABJ(M) model. This is a level k Chern-Simons theory, described in terms of the two gauge fields A and Awhich couple to a matter sector given by bi-fundamental complex scalars CI , CJ and fermions ψI , ψJ (with I, J = 1, . . . 4). The geometric angle Bremsstrahlung B1φ/6 has been directly computed up to two loops [12, 18] and a conjecture for its all-loop expression has been given in [13, 15]. This agrees with the strong coupling result up to the sub-leading order [19, 20]. The internal angle Bremsstrahlung function B1θ/6(k, N ), has been computed at weak coupling at two- [18] and four-loop orders in the planar limit [13]. In this paper we provide a striking test of (2.4) by computing the full non-planar B1θ/6(k, N ) at four loops and comparing it with the conjectural form of B1φ/6(k, N )
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