Flux Vacua, Asymptotic Periods, and Relatively Anosov Representations

Abstract

We develop a topological method to detect classical flux vacua of M-theory on Calabi-Yau fourfolds with a single complex structure modulus using only asymptotic period data and monodromy information. To this end, we express the index of the F-term of the flux superpotential as a winding number along the boundary of the universal cover of the complex structure moduli space. The index evaluates to a sum over zeros and poles of a suitably normalized boundary F-term, where local contributions can be computed algebraically on a dense set of boundary points. Assuming a conjectured bound on the remaining contributions, sufficiently many sign changes of the boundary F-term guarantee a flux vacuum in the interior. We illustrate the method on the mirror Fermat sextic with explicit examples and a systematic flux scan. A main technical ingredient in our construction is a continuity result for projective period maps: we prove that the non-holomorphic (3,1)-period map extends continuously to the boundary of the covering space if the monodromy representation is relatively Anosov. In general, this property does not hold for holomorphic (4,0)-periods.

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BibTeX RIS

BibTeX

@misc{balavoine2026flux,
  title = {{Flux Vacua, Asymptotic Periods, and Relatively Anosov Representations}},
  author = {Paul Balavoine and Severin Lüst},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27077},
  eprint = {2610.27077},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27077},
}

RIS

TY  - UNPB
TI  - Flux Vacua, Asymptotic Periods, and Relatively Anosov Representations
AU  - Paul Balavoine
AU  - Severin Lüst
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27077
UR  - https://arxiv.org/abs/2610.27077
AB  - We develop a topological method to detect classical flux vacua of M-theory on Calabi-Yau fourfolds with a single complex structure modulus using only asymptotic period data and monodromy information. To this end, we express the index of the F-term of the flux superpotential as a winding number along the boundary of the universal cover of the complex structure moduli space. The index evaluates to a sum over zeros and poles of a suitably normalized boundary F-term, where local contributions can be computed algebraically on a dense set of boundary points. Assuming a conjectured bound on the remaining contributions, sufficiently many sign changes of the boundary F-term guarantee a flux vacuum in the interior. We illustrate the method on the mirror Fermat sextic with explicit examples and a systematic flux scan. A main technical ingredient in our construction is a continuity result for projective period maps: we prove that the non-holomorphic (3,1)-period map extends continuously to the boundary of the covering space if the monodromy representation is relatively Anosov. In general, this property does not hold for holomorphic (4,0)-periods.
ER  -

Abstract

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