Beyond the polynomial ansatz: regular AdS3× M8 solutions of M-theory
Abstract
We study regular compact solutions of the cohomogeneity-one AdS3× M8 system of Gauntlett, Mac Conamhna, Mateos and Waldram, where M8 is an S2 bundle over three constant-curvature Riemann surfaces. We find that an endpoint argument rules out every non-flat curvature-sign sector without a positive-curvature factor, while an analytic deformation gives regular families with four radial shape parameters in all remaining sectors, with the base geometry held fixed. The known polynomial solutions form a proper analytic locus in these families. Non-polynomiality is therefore generic in parameter space, although the deviation from an endpoint-matching polynomial can be very small. Apart from the completely flat exception, the curvature-sign criterion is necessary and sufficient within this ansatz. Four magnetic flux ratios give local coordinates near the reference solution and its small-curvature deformations, and a rational inverse reconstructs candidate endpoint data directly from finite flux ratios. In the fully positive sector we prove that one explicit four-dimensional finite-ratio neighbourhood lies inside the physical flux image. The magnetic periods and leading holographic central charge reduce to endpoint data, and, once the common Brown--Henneaux normalization is fixed, the nontrivial flux dependence of the equivariant localization formula agrees with the endpoint result as an exact algebraic identity. We also quantify the non-polynomial corrections and analyse finite degenerations under explicit convergence hypotheses.
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BibTeX
@misc{gregory2026beyond,
title = {{Beyond the polynomial ansatz: regular $AdS_3\times M_8$ solutions of M-theory}},
author = {Carolina Matté Gregory},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20853},
eprint = {2610.20853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20853},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond the polynomial ansatz: regular AdS_3× M_8 solutions of M-theory
AU - Carolina Matté Gregory
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20853
UR - https://arxiv.org/abs/2610.20853
AB - We study regular compact solutions of the cohomogeneity-one AdS_3× M_8 system of Gauntlett, Mac Conamhna, Mateos and Waldram, where M_8 is an S^2 bundle over three constant-curvature Riemann surfaces. We find that an endpoint argument rules out every non-flat curvature-sign sector without a positive-curvature factor, while an analytic deformation gives regular families with four radial shape parameters in all remaining sectors, with the base geometry held fixed. The known polynomial solutions form a proper analytic locus in these families. Non-polynomiality is therefore generic in parameter space, although the deviation from an endpoint-matching polynomial can be very small. Apart from the completely flat exception, the curvature-sign criterion is necessary and sufficient within this ansatz. Four magnetic flux ratios give local coordinates near the reference solution and its small-curvature deformations, and a rational inverse reconstructs candidate endpoint data directly from finite flux ratios. In the fully positive sector we prove that one explicit four-dimensional finite-ratio neighbourhood lies inside the physical flux image. The magnetic periods and leading holographic central charge reduce to endpoint data, and, once the common Brown--Henneaux normalization is fixed, the nontrivial flux dependence of the equivariant localization formula agrees with the endpoint result as an exact algebraic identity. We also quantify the non-polynomial corrections and analyse finite degenerations under explicit convergence hypotheses.
ER -