Non-critical M-Theory and the Resolved Conifold: Refinement and Nonperturbative Completion

@misc{xu2026noncritical,
  title = {{Non-critical M-Theory and the Resolved Conifold: Refinement and Nonperturbative Completion}},
  author = {Fengjun Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06075},
  eprint = {2609.06075},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06075},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Non-critical M-Theory and the Resolved Conifold: Refinement and Nonperturbative Completion
AU  - Fengjun Xu
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06075
UR  - https://arxiv.org/abs/2609.06075
AB  - We extend the Hořava--Keeler correspondence between finite-temperature non-critical M-theory and the resolved-conifold A-model to the refined theory. The grand potential of the stationary rotating non-critical M-theory vacuum reproduces the refined Gopakumar--Vafa expansion, with the angular chemical potential deforming the Ω-background away from the self-dual locus eps_1=−eps_2. At finite thermal radius, we establish an exact match with the nonperturbative conifold completions proposed by Hattab--Palti and by Chuang in the unrefined and refined cases, respectively. Both the one-particle Schwinger integrand and its integration cycle arise from the non-critical M-theory spectrum and resolvent, providing a microscopic spectral realization of these completions. The correspondence fixes the nonconstant BPS sector and the cubic local contribution, while the remaining polynomial ambiguity and the modulus-independent constant-map sector require separate normalization. We explain why the single primitive spinless multiplet of the resolved conifold makes this identification possible, and discuss what additional charge- and spin-dependent microscopic data would be needed for an extension to more general local Calabi--Yau geometries.
ER  -