Exact Bremsstrahlung functions in ABJM theory

Abstract

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 ϕ 1/6 ) and R-symmetry (B θ 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 θ 1/6 based on a known result for B ϕ 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(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.

Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations

“…It would be interesting to study the interpolating Wilson loop perturbatively as in [22] and also to compute higher point holographic correlators as in [36]. The study of correlators in defect CFT's defined by ABJM Wilson lines [37,38] could be extended to the whole family of interpolating Wilson loops. Similarly, the setup becomes adequate to study integrability aspects of this interpolating Wilson loop not only from the gravity side but also from the field theory as was done for N = 4 SYM case in [39].…”

Roadmap on Wilson loops in 3d Chern–Simons-matter theories

“…The smaller amount of preserved supersymmetry naively prevents one from relating B ϕ 1/6 and B θ 1/6 using defect supersymmetric Ward identities (in this case D and O do not belong to the same supermultiplet as it happens for the 1/2 BPS case). Nevertheless, it was shown in [76] that a class of vanishing three-point functions allows to write Ward identities with broken supercharges giving a formal derivation of the relation…”

Toward precision holography in type IIA with Wilson loops

“…The beautiful result above is the culmination of an impressive series of papers [23][24][25][26] (see also [27,28] [29].…”

“…In the expansion scheme of (5.5), the corresponding perturbative operator is 28) for the bosonic second order operators. While, for the first order fermionic operator, we have,…”