The warp factor of supersymmetric D=11 near-horizon geometries: single-point rigidity, the Spin(7) perfect square, and global constraints
Abstract
On a compact connected section cal S of a supersymmetric M-horizon the Killing-spinor bilinears give a pointwise identity relating the warp factor Δ, the rotation one-form h and the two spinor norms, with nothing assumed about the norm of the Killing spinor. We derive three consequences of that unreduced identity. First, a single-point rigidity theorem: if Δ and h vanish at one point of the section, then the flux vanishes identically, cal S is Ricci-flat and the horizon is ℝ1,1×cal S. A single point replaces the usual global spinorial hypothesis. Second, the Spin(7) decomposition of the flux fixes h algebraically and exhibits the invariant flux content of the scalar square Δ=4Φ2 known in an adapted gauge, Δ=1/108|wbf 7±σ(cal Ybf 7)|2. Only the two bf 7-summands wbf 7, cal Ybf 7 reach the warp factor, and the square is degenerate rather than definite: it vanishes on the linear subspace wbf 7=∓σ(cal Ybf 7) rather than at the origin, so positivity of Δ yields no case list. Third, the two combine into a pointwise budget: the single constant of supersymmetry is shared between the deviation from staticity and the Spin(7) mismatch of the flux, each bounded by that constant. The same identities characterise the constancy hypothesis, equivalent to V=−fh for the bilinear one-form V, which fails on the static branch of known warped AdS2 solutions; they fix a weighted integral of the warp factor; and they reduce the Komar angular momentum of the horizon to a positive bilinear integral. Two no-go statements, for hidden symmetries built from the Killing spinor and for a second isometry from its bilinears, are stated with their hypotheses.
Related
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BibTeX
@misc{kayani2026warp,
title = {{The warp factor of supersymmetric $D=11$ near-horizon geometries: single-point rigidity, the $Spin(7)$ perfect square, and global constraints}},
author = {Usman Kayani},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29879},
eprint = {2608.29879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29879},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The warp factor of supersymmetric D=11 near-horizon geometries: single-point rigidity, the Spin(7) perfect square, and global constraints
AU - Usman Kayani
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29879
UR - https://arxiv.org/abs/2608.29879
AB - On a compact connected section cal S of a supersymmetric M-horizon the Killing-spinor bilinears give a pointwise identity relating the warp factor Δ, the rotation one-form h and the two spinor norms, with nothing assumed about the norm of the Killing spinor. We derive three consequences of that unreduced identity. First, a single-point rigidity theorem: if Δ and h vanish at one point of the section, then the flux vanishes identically, cal S is Ricci-flat and the horizon is ℝ^1,1×cal S. A single point replaces the usual global spinorial hypothesis. Second, the Spin(7) decomposition of the flux fixes h algebraically and exhibits the invariant flux content of the scalar square Δ=4Φ^2 known in an adapted gauge, Δ=1/108|w_bf 7±σ(cal Y_bf 7)|^2. Only the two bf 7-summands w_bf 7, cal Y_bf 7 reach the warp factor, and the square is degenerate rather than definite: it vanishes on the linear subspace w_bf 7=∓σ(cal Y_bf 7) rather than at the origin, so positivity of Δ yields no case list. Third, the two combine into a pointwise budget: the single constant of supersymmetry is shared between the deviation from staticity and the Spin(7) mismatch of the flux, each bounded by that constant. The same identities characterise the constancy hypothesis, equivalent to V=−fh for the bilinear one-form V, which fails on the static branch of known warped AdS_2 solutions; they fix a weighted integral of the warp factor; and they reduce the Komar angular momentum of the horizon to a positive bilinear integral. Two no-go statements, for hidden symmetries built from the Killing spinor and for a second isometry from its bilinears, are stated with their hypotheses.
ER -