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arXiv · 2609.06075

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

Fengjun Xu
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Abstract

We extend the Ho\v{r}ava--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 $\Omega$-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.

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Fengjun Xu. 2026-09-05. Non-critical M-Theory and the Resolved Conifold: Refinement and Nonperturbative Completion. https://arxiv.org/abs/2609.06075

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