Instantons from geometry in M2-brane sphere partition functions
Abstract
Can the geometry transverse to M2-branes capture effects that are exponentially small in their three-sphere (S3) partition function? We investigate this question by extending beyond constant maps the proposal that M2-brane observables are encoded by equivariant topological strings on the transverse Calabi-Yau fourfold (CY4). Our central object is the disk partition function of the CY4 gauged linear sigma model, a quantum generalization of the equivariant volume. After a Gamma-function normalization and a Mellin transform, it reproduces the complete leading WKB grand potential in the examples admitting a suitable Fermi-gas description, including the R-charge and mass deformations compatible with that description. In particular, the transform recovers membrane-instanton series even for ℂ4, which has no compact curves. For resolved CY4 cones with compact curves, the match requires a quantum refinement of the classical mesonic constraint. We establish the exact equalities of the corresponding dressed disk partition functions with the classical spectral traces for ABJM, ADHM and a representative set of flavored M2-brane quiver theories. Away from the deformation loci where this match can be established, the same construction yields geometric predictions for the membrane-instanton sector that remain to be tested.
Related
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- Finding CFTs from spatial positivity of partition functions
- Trace Relations and Partition Functions
- From Z to all: cyclic sum rules for thermal CFT partition functions
BibTeX
@misc{hristov2026instantons,
title = {{Instantons from geometry in M2-brane sphere partition functions}},
author = {Kiril Hristov and Ali Mert Yetkin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07186},
eprint = {2611.07186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07186},
}
RIS
TY - UNPB
TI - Instantons from geometry in M2-brane sphere partition functions
AU - Kiril Hristov
AU - Ali Mert Yetkin
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07186
UR - https://arxiv.org/abs/2611.07186
AB - Can the geometry transverse to M2-branes capture effects that are exponentially small in their three-sphere (S^3) partition function? We investigate this question by extending beyond constant maps the proposal that M2-brane observables are encoded by equivariant topological strings on the transverse Calabi-Yau fourfold (CY_4). Our central object is the disk partition function of the CY_4 gauged linear sigma model, a quantum generalization of the equivariant volume. After a Gamma-function normalization and a Mellin transform, it reproduces the complete leading WKB grand potential in the examples admitting a suitable Fermi-gas description, including the R-charge and mass deformations compatible with that description. In particular, the transform recovers membrane-instanton series even for ℂ^4, which has no compact curves. For resolved CY_4 cones with compact curves, the match requires a quantum refinement of the classical mesonic constraint. We establish the exact equalities of the corresponding dressed disk partition functions with the classical spectral traces for ABJM, ADHM and a representative set of flavored M2-brane quiver theories. Away from the deformation loci where this match can be established, the same construction yields geometric predictions for the membrane-instanton sector that remain to be tested.
ER -