Blackened BPS: the end of the thermal BMN branch
Abstract
We study the thermodynamics of the BMN matrix model at large N and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional SO(9) gauged supergravity, the static SO(3)× SO(6)-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of μ/T, which power-law fits place at 4π with an estimated uncertainty below 10−10. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the 2/5 power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.
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BibTeX
@misc{santos2026blackened,
title = {{Blackened BPS: the end of the thermal BMN branch}},
author = {Jorge E. Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02305},
eprint = {2610.02305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Blackened BPS: the end of the thermal BMN branch
AU - Jorge E. Santos
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02305
UR - https://arxiv.org/abs/2610.02305
AB - We study the thermodynamics of the BMN matrix model at large N and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional SO(9) gauged supergravity, the static SO(3)× SO(6)-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of μ/T, which power-law fits place at 4π with an estimated uncertainty below 10^−10. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the 2/5 power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.
ER -