Abstract
In this paper we study the Bremsstrahlung functions for the frac{1}{6}mathrm{B}mathrm{P}mathrm{S} and the frac{1}{2}mathrm{B}mathrm{P}mathrm{S} 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 (B1/6φ) and R-symmetry (B1/6θ) deformations of the frac{1}{6}mathrm{B}mathrm{P}mathrm{S} Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for B1/6θ based on a known result for B1/6φ. Subsequently, we explore the consequences of this relation for the frac{1}{2}mathrm{B}mathrm{P}mathrm{S} 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(λ). During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.
Highlights
Introduction and resultsExact results for interacting quantum field theories are notoriously hard to achieve
We focus on a particular choice for the contour in order to define the cusp anomalous dimensions and the Bremsstrahlung functions summarizing the state of the art in the literature
We summarize the relations between the supersymmetric Wilson loops above as follows
Summary
Exact results for interacting quantum field theories are notoriously hard to achieve. For ABJM, two different generalized cusps may be defined for the bosonic and fermionic Wilson lines [39, 40] While for the former no residual BPS configuration could be found, for the latter the specific case φ2 = θ2 still preserves two supercharges, such that Γ1cu/s2p(φ, ±φ) vanishes. Which is the analogue of the four-dimensional case This fact, supported by a three-loop computation, led to the conjecture of a relation between the Bremsstrahlung function and the first-order supersymmetric deformation of the circular. The residual symmetry can be used to constrain defect correlation functions of local operators inserted along the Wilson line Such insertions are organized in irreducible representations of the preserved subalgebra: long multiplets, whose scaling dimension is not protected, and short multiplets which are annihilated by one of the two preserved supercharges and whose dimension is fixed by algebraic arguments. Few appendices follow, which contain conventions and some details of the supermultiplets and the supersymmetry algebra
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