Quark-anti-quark potential in N $$ \mathcal{N} $$ = 4 SYM

Gromov, Nikolay; Levkovich-Maslyuk, Fedor

doi:10.1007/jhep12(2016)122

Cited by 47 publications

(47 citation statements)

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“…It would be very interesting to see whether it is possible -as it is the case for the cusp anomalous dimension in N = 4 SYM theory -to calculate the cross anomalous dimension or limits thereof based on localization [29] or integrability [30], see also refs. [31] for recent developments on the cusp anomalous dimension. The cross anomalous dimension provides a richer structure than the cusp anomalous dimension (e.g.…”

Section: Discussionmentioning

confidence: 99%

The cross anomalous dimension in maximally supersymmetric Yang-Mills theory

Münkler¹

2018

J. High Energ. Phys.

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The cross or soft anomalous dimension matrix describes the renormalization of Wilson loops with a self-intersection and is an important object in the study of infrared divergences of scattering amplitudes. In this paper it is studied for the Maldacena-Wilson loop in N = 4 supersymmetric Yang-Mills theory and Euclidean kinematics. We consider both the strong-coupling description in terms of minimal surfaces in AdS 5 as well as the weak-coupling side up to the two-loop level. In either case, the coefficients of the cross anomalous dimension matrix can be expressed in terms of the cusp anomalous dimension. The strong-coupling description displays a Gross-Ooguri phase transition and we argue that the cross anomalous dimension is an interesting object to study in an integrability-based approach.

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Section: Discussionmentioning

confidence: 99%

The cross anomalous dimension in maximally supersymmetric Yang-Mills theory

Münkler¹

2018

J. High Energ. Phys.

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“…Fitting (tree-level-improved [127]) lattice data to the Coulomb potential V (r) = A − C/r predicts the Coulomb coefficient C(λ) shown in the figure. There is a famous holographic prediction [128,129] that in the regime N → ∞ and λ → ∞ with λ N this quantity should behave as C(λ) ∝ √ λ up to O 1 √ λ corrections, and more general analytic results have been obtained in the N = ∞ planar limit [130]. The lattice results for N ≤ 4 and λ lat ≤ 2 do not show such behavior and instead look consistent with leading-order perturbation theory.…”

Section: Maximally Supersymmetric Yang-mills (N = 4 Sym) In Four Dimementioning

confidence: 94%

Progress and prospects of lattice supersymmetry

Schaich¹

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a nonperturbative regularization suitable for strongly interacting systems. Lattice investigations of supersymmetric field theories are currently making significant progress, though many challenges remain to be overcome. In this brief overview I discuss particularly notable progress in three areas: supersymmetric Yang-Mills (SYM) theories in fewer than four dimensions, as well as both minimal N = 1 SYM and maximal N = 4 SYM in four dimensions. I also highlight super-QCD and sign problems as prominent challenges that will be important to address in future work. Progress and prospects of lattice supersymmetry David Schaich Introduction, motivation and backgroundSupersymmetry plays prominent roles in modern theoretical physics, as a tool to improve our understanding of quantum field theory (QFT), as an ingredient in many new physics models, and as a means to study quantum gravity via holographic duality. Lattice field theory provides a nonperturbative regularization for QFTs, and other contributions to these proceedings document the prodigious success of this framework applied to QCD and similar theories. It is natural to consider employing lattice field theory to investigate supersymmetric QFTs, especially in strongly coupled regimes. In this proceedings I review the recent progress and future prospects of lattice studies of supersymmetric systems, focusing on four-dimensional gauge theories and their dimensional reductions to d < 4. 1 Lattice supersymmetry now has more than four decades of history [1], much of which is reviewed by Refs. [2 -7]. Unfortunately, progress in this field has been slower than for QCD, in large part because the lattice discretization of space-time breaks supersymmetry. This occurs in three main ways. First, the anti-commutation relation Q α , Qα = 2σ µ αα P µ in the super-Poincaré algebra connects the spinorial generators of supersymmetry transformations, Q α and Qα, to the generator of infinitesimal space-time translations, P µ . The absence of infinitesimal translations on the lattice consequently implies broken supersymmetry.Next, bosonic and fermionic fields are typically discretized differently on the lattice (in part due to the famous fermion doubling problem). In the specific context of supersymmetric gauge theories, standard discretizations associate the gauginos with lattice sites n (i.e., they transform as G(n)λ α (n)G † (n) under a lattice gauge transformation) while the gauge connections are associated with links between nearest-neighbor sites, transforming as G(n)U µ (n)G † (n + a µ) where 'a' is the lattice spacing. Away from the a → 0 continuum limit, these differences prevent supersymmetry transformations from correctly interchanging superpartners.Finally, supersymmetry requires a derivative operator that obeys the Leibniz rule [1], viz. ∂ [φη] = [∂φ] η + φ∂η, which is violated by standard la...

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“…An important feature of such models is the drastic simplification of their weak coupling expansion, where in many particular cases (when we turn on a single coupling) it is dominated by various kinds of "fishnet" Feynman graphs [43]. These graphs represent integrable two-dimensional statisticalmechanical systems by themselves [48] and can be efficiently studied by the quantum spin chain methods and the double-scaled version QSC [44,49]. In particular, the individual, so called "wheel" multi-loop Feynman graphs can be computed exactly in terms of multiple zeta values (MZV) [44].…”

Section: Introductionmentioning

confidence: 99%

Exact correlation functions in conformal fishnet theory

Gromov

Казаков

Korchemsky

2019

J. High Energ. Phys.

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179

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We compute exactly various 4−point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin. In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator. We show that at weak coupling 4−point correlation functions can be systematically expanded in terms of harmonic polylogarithm functions and verify our results by explicit calculation of Feynman graphs at a few orders in the coupling. At strong coupling we obtain that the correlation functions exhibit the scaling behaviour typical for semiclassical description hinting at the existence of the holographic dual. 1 Unité Mixte de Recherche 3681 du CNRS arXiv:1808.02688v1 [hep-th] 8 Aug 20181 In the literature one also uses notations φ 1 = X and φ 2 = Z. We use 'bar' for the Hermitian conjugation.

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Quark-anti-quark potential in N $$ \mathcal{N} $$ = 4 SYM

Cited by 47 publications

References 46 publications

The cross anomalous dimension in maximally supersymmetric Yang-Mills theory

The cross anomalous dimension in maximally supersymmetric Yang-Mills theory

Progress and prospects of lattice supersymmetry

Exact correlation functions in conformal fishnet theory

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