A critical coupling for the magnetic instability of holographic SU(2) plasmas
Abstract
We show that gravity can remove the linear magnetic instability of a holographic plasma with an SU(2) global symmetry. In the probe limit, charged vector bosons become tachyonic in their lowest Landau level above a critical field and condense into a vortex lattice. In Einstein-SU(2) Yang-Mills theory in AdS5 we include the backreaction of the field exactly, expanding only in the condensate around the D'Hoker-Kraus magnetic brane. The critical field diverges as the coupling α= κ2/ĝ2 approaches α⋆ = 2/3, above which the normal phase has no linear charged instability at any field or temperature: we show this at zero temperature and establish it numerically at finite temperature. At zero temperature the field cancels from the mass of the lowest Landau level in the brane's AdS3 × ℝ2 throat, and the instability is a violation of the throat's Breitenlohner-Freedman bound. The onset temperature vanishes at α⋆ with an essential singularity of Berezinskii-Kosterlitz-Thouless type. For two-derivative Einstein-Yang-Mills duals in d = 4, 5 and 6 dimensions the normal phase has a charged instability if and only if CJ/CT < 8/(d2(d+1)), one tenth in d = 4. Above αL = 0.372 the gravitational attraction between vortices makes the uniform lattice unstable and the transition first order, so Bc is only a spinodal; whether a condensed phase survives above α⋆ is left open.
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BibTeX
@misc{strydom2026critical,
title = {{A critical coupling for the magnetic instability of holographic SU(2) plasmas}},
author = {Migael Strydom},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14675},
eprint = {2610.14675},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14675},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A critical coupling for the magnetic instability of holographic SU(2) plasmas
AU - Migael Strydom
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14675
UR - https://arxiv.org/abs/2610.14675
AB - We show that gravity can remove the linear magnetic instability of a holographic plasma with an SU(2) global symmetry. In the probe limit, charged vector bosons become tachyonic in their lowest Landau level above a critical field and condense into a vortex lattice. In Einstein-SU(2) Yang-Mills theory in AdS_5 we include the backreaction of the field exactly, expanding only in the condensate around the D'Hoker-Kraus magnetic brane. The critical field diverges as the coupling α= κ^2/ĝ^2 approaches α_⋆ = 2/3, above which the normal phase has no linear charged instability at any field or temperature: we show this at zero temperature and establish it numerically at finite temperature. At zero temperature the field cancels from the mass of the lowest Landau level in the brane's AdS_3 × ℝ^2 throat, and the instability is a violation of the throat's Breitenlohner-Freedman bound. The onset temperature vanishes at α_⋆ with an essential singularity of Berezinskii-Kosterlitz-Thouless type. For two-derivative Einstein-Yang-Mills duals in d = 4, 5 and 6 dimensions the normal phase has a charged instability if and only if C_J/C_T < 8/(d^2(d+1)), one tenth in d = 4. Above α_L = 0.372 the gravitational attraction between vortices makes the uniform lattice unstable and the transition first order, so B_c is only a spinodal; whether a condensed phase survives above α_⋆ is left open.
ER -