Abstract
Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects. We focus on a holographic model which has the same global symmetry as that of low energy plasma and obtain the lifetime of (non-conserved) electric flux in a strong magnetic field regime. The lifetime is inversely correlated to the magnetic field strength and thus suppressed in the strong field regime.
Highlights
With the lifetime of the electric field τE = 1/σ
Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects
The conserved currents T μν and Jμν are expressed in terms of energy, momentum, magnetic flux Jti ≡ Bi and their conjugates, organised order by order in the gradient expansion. This formulation of MHD only requires macroscopic consistency and does not require the introduction of the gauge field J = F = dA which, due to screening effect, is not a long-lived degree of freedom. This brings us to the central question of the present paper: is a hydrodynamic description of the form (1.3) applicable in the limit low temperature compared to magnetic flux density T 2/|B| 1? This question is important if one wants to apply the MHD description to astrophysical plasmas where the magnetic field is many orders of magnitude larger than the scale set by the temperature
Summary
A simple holographic dual to a strongly interacting field theory of matter charged under dynamical U(1) electromagnetism (that is, the dynamical plasma described by low energy MHD) and formulated in the language of higher-form symmetry was constructed in [27, 28]. Requiring the source bμν to be independent of the UV cutoff fixes the form of the ‘coupling constant’ 1/κ(Λ) which turns out to be logarithmically running This is a common feature for fields with this type of near-boundary behaviour where the counterterm plays the role of the double-trace deformation [38, 39], see [27, 28] for a discussion in the present context. While the finite counterterm in the ordinary bulk Maxwell theory results in a contact term in the correlation function, the mixed boundary condition for Bab implies the existence of the purely decaying mode ω = −i/τE that can interfere with the gapless hydrodynamic excitation This is nothing but the life-time of the electric flux operator QE ∼ dSijJij which appears in the following correlation function [28, 34]. We present the key equations and resulting lifetime of the electric flux
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