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In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{varphi}_{1/6}$) and R-symmetry ($B^{theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{theta}_{1/6}$ based on a known result for $B^{varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.
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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.
We construct a class of operators, given by Schur polynomials, in ABJM theory. By computing two point functions at finite $N$ we confirm these are diagonal for this class of operators in the free field limit. We also calculate exact three and multi point correlators in the zero coupling limit. Finally, we consider a particular nontrivial background produced by an operator with an $R$-charge of $O(N^2$. We show that the nonplanar corrections (which can no longer be neglected, even at large $N$) can be resummed to give a $1/(N+M)$ expansion for correlators computed in this background.
In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS Wilson line by introducing an angle $varphi$ in the spacial contour and/or an angle $theta$ in the internal R-symmetry space. The small angles limits of its anomalous dimension are controlled by corresponding Bremsstrahlung functions. In this note we compute the internal space $theta$-Bremsstrahlung function to four loops at weak coupling in the planar limit. Based on this result, we propose an all order conjecture for the $theta$-Bremsstrahlung function.
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.
We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.
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