Polyakov’s confinement mechanism for generalized Maxwell theory

Heydeman, Matthew; Jepsen, Christian Baadsgaard; Ji, Ziming; Yarom, Amos

doi:10.1007/jhep04(2023)119

Cited by 6 publications

(3 citation statements)

References 87 publications

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“…There is also a recently developed lattice bootstrap method from [93] which gave good results for the non-critical SRI. Applying this to the LRI is another possible future direction considering the interesting phase structure that can exist for nonlocal QFTs [94]. Some of these have been studied with the functional renormalization group in [85,95].…”

Section: Discussionmentioning

confidence: 99%

Analytic and numerical bootstrap for the long-range Ising model

Behan,

Lauria,

Nocchi

et al. 2024

J. High Energ. Phys.

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We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

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Section: Discussionmentioning

confidence: 99%

Analytic and numerical bootstrap for the long-range Ising model

Behan,

Lauria,

Nocchi

et al. 2024

J. High Energ. Phys.

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“…4 A different point of view is to ask how these electromagnetic interactions between the charged matter could be reproduced by a purely three dimensional field theory. The answer is a non-local electromagnetism, as explored here [23,24]. 5 More generally, 2πJ = 2π g 2 E + θ 2π B, and we can also define 2πI = B.…”

Section: Jhep05(2024)235mentioning

confidence: 98%

Bootstrapping boundary QED. Part I

Bartlett-Tisdall,

Herzog,

Schaub

2024

J. High Energ. Phys.

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We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary conformal field theory with an exactly marginal coupling corresponding to the strength of the interaction between the photon and the matter degrees of freedom. In part one of this project, we present three results. We show how the Maxwell equations put severe constraints on boundary three-point functions involving two currents and a symmetric traceless tensor. We use semi-definite programming to show that any three dimensional conformal field theory with a global U(1) symmetry must have a spin two gap less than about 1.05. Finally, combining a numerical bound on an OPE coefficient and some Ward identities involving the current and the displacement operator, we bound the displacement operator two-point function above. This upper bound also constrains a boundary contribution to the anomaly in the trace of the stress tensor for these types of theories.

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“…The fractional Laplacian is a non-local pseudo-differential operator that has recently been used to model and investigate a wide range of physical and mathematical physical systems [1]. Models based on the fractional Laplacian have been successfully used to analyze the absorption and dispersion of compressional and shear waves in viscoelastic solids [2], fractional diffusion theory [3], non-linear fractional MOND-like gravity [4] and the Kuzmin-like gravitational model [5], the Scott correction for few electrons in atoms [6,7], the non-locality of the Pippard kernel in superconductivity and anomalous dimension for holographic conserved currents [8], long-distance processes that characterize tracer transport in both subsurface and surface environments [9], Polyakov's confinement mechanism for Maxwell's equations [10], soliton stabilization in d = 1 with possible applications to Bose-Einstein condensates [11], solitonic solutions to the non-linear Schroedinger equation [12], the quantization of non-local scalar fields with an extension problem [13], the conformal invariance in the long-range Ising model [14] and non-local scalar fields with an extension problem [15], just to mention a few applications across the spectrum of physics.…”

Section: Introductionmentioning

confidence: 99%

Fractional Laplacian Spinning Particle in External Electromagnetic Field

Porto,

Godinho,

Vancea

2023

Dynamics

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We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable λ governs the kinetic energy that is non-local in λ. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in λ, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

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Polyakov’s confinement mechanism for generalized Maxwell theory

Cited by 6 publications

References 87 publications

Analytic and numerical bootstrap for the long-range Ising model

Analytic and numerical bootstrap for the long-range Ising model

Bootstrapping boundary QED. Part I

Fractional Laplacian Spinning Particle in External Electromagnetic Field

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