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

Drukker, Nadav; Trancanelli, Diego; Bianchi, Lorenzo; Bianchi, Marco S.; Correa, Diego H.; Форини, Валентина; Griguolo, Luca; Leoni, Matías; Levkovich-Maslyuk, Fedor; Nagaoka, Gabriel; Penati, Silvia; Preti, Michelangelo; Probst, Malte; Putrov, Pavel; Seminara, Domenico; Silva, Guillermo; Tenser, Marcia; Trépanier, Maxime; Vescovi, Edoardo; Yaakov, Itamar; Zhang, Jiaju

doi:10.1088/1751-8121/ab5d50

Cited by 63 publications

(120 citation statements)

References 217 publications

(577 reference statements)

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“…For ABJM one can again compute the small S expansion analytically which led to a conjecture for the exact form of the function h(λ) appearing in all integrability-based results for ABJM [70]. That conjecture was later extended to ABJ theory [71] (see also the recent review [72] for a recent related review).…”

Section: Highlights Of Qsc-based Resultsmentioning

confidence: 94%

A review of the AdS/CFT Quantum Spectral Curve

Levkovich-Maslyuk¹

2020

J. Phys. A: Math. Theor.

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We give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a Riemann-Hilbert problem for a finite set of functions. We review the underlying QQ relations starting from simple spin chain examples, and describe the special features arising for AdS/CFT. We also discuss the recently found links between the Quantum Spectral Curve and the computation of correlation functions. To appear in a special issue of J. Phys. A based on lectures given at the Young Researchers Integrability School and Workshop 2018. * We will not present the original derivation of the QSC from other approaches such as TBA [29], since it is rather technical and in any case applies only for some subsets of states (for which the TBA is well understood). Instead we will present the final result and describe its algebraic structure, starting from simpler spin chains as a motivating example.

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Section: Highlights Of Qsc-based Resultsmentioning

confidence: 94%

A review of the AdS/CFT Quantum Spectral Curve

Levkovich-Maslyuk¹

2020

J. Phys. A: Math. Theor.

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“…(5.21) 10 We normalize the flat measure as da = c da c / √ 2π , so that da e − tr a 2 = 1. In this way the contraction (5.20) immediately follows.…”

Section: Perturbative Expansionmentioning

confidence: 99%

“…Furthermore, the same quantity can be related to the small angle limit of the cusp anomalous dimension, thus providing an interesting connection with massive scattering amplitudes.Similar developments allowed to find an exact expression for the Bremsstrahlung function in ABJM theory [9], a three-dimensional relative of N = 4 SYM. In that case, two superconformal Wilson lines are known (see [10] for a recent review). The immediate generalization of the Maldacena Wilson loop turns out to be 1 6 BPS [11-13] and its Bremsstrahlung function was already proposed in [14].…”

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confidence: 99%

Emitted radiation and geometry

Bianchi

Billó

Galvagno

et al. 2020

J. High Energ. Phys.

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In conformal N = 2 Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter. Keywords: N = 2 conformal SYM theories, Wilson loops, Brehmsstrahlung, rigid supersymmetry dimensions has no scale, thus the straight Wilson line can be treated as a conformal defect. The emitted radiation is computed by slightly deforming the shape of the defect.As usual, things get harder when one considers non-Abelian gauge theories, which are strongly coupled at low energies and where conformality is broken by quantum corrections. In light of this complexity, it is useful to restrict our attention to those examples of strongly interacting gauge theories which preserve conformality. These cases typically come with a larger symmetry group which includes supersymmetry, making them much more tractable. For the maximally supersymmetric theory in four dimensions, N = 4 Super Yang Mills (SYM) theory, the combination of defect techniques and supersymmetric localization led to the derivation of a beautiful formula for the Bremsstrahlung function associated with the Maldacena Wilson loop [1,2], preserving half of the supercharges. Shortly after, the same result was confirmed by an integrability computation [3,4], providing one of the few examples of a quantity that is accessible to both techniques 1 . The work of [1] heavily relied on the interpretation of the Wilson line as a superconformal defect. In particular, it was pointed out that the Bremsstrahlung function can be computed as the two-point function of an important defect operator, called the displacement operator. Furthermore, the same quantity can be related to the small angle limit of the cusp anomalous dimension, thus providing an interesting connection with massive scattering amplitudes.Similar developments allowed to find an exact expression for the Bremsstrahlung function in ABJM theory [9], a three-dimensional relative of N = 4 SYM. In that case, two superconformal Wilson lines are known (see [10] for a recent review). The immediate generalization of the Maldacena Wilson loop turns out to be 1 6 BPS [11-13] and its Bremsstrahlung function was already proposed in [14]. The maximally supersymmetric case [15], instead, involves also fermionic couplings ...

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“…For the case of Wilson loops in N = 6 super Chern-Simons-matter or ABJM theory, the dual open strings propagate in AdS 4 × CP 3 and the consideration of mixing boundary conditions leads to various interesting distinctions with respect to the N = 4 super Yang-Mills case. To begin with, there are two distinct locally supersymmetric Wilson loops in ABJM with the same string dual: the 1/2 BPS Wilson loops [12], coupled to gauge fields, scalars and fermions, and the bosonic 1/6 BPS Wilson loop coupled solely to scalars [13,14,15] (see [16] for a recent review on ABJM Wilson loops). The dual open string of the former has Dirichlet boundary conditions in all CP 3 coordinates, while the latter's dual string has Neumann boundary conditions for some CP 1 ⊂ CP 3 and Dirichlet for the rest.…”

Section: Introductionmentioning

confidence: 99%