Asymptotic limits in class-𝒮 theories and non-Abelian Hodge theory
Abstract
We develop a non-Abelian Hodge-theoretic refinement of asymptotic limits in type-A class-𝒮 theories, enriching the geometric description of the degenerating UV curve with gauge-theoretic data encoded by the associated Hitchin system. A degeneration of the UV curve produces a long plumbing tube, which we equip with the local monodromy data of a Hitchin-Simpson flat connection admitting a regular-singular logarithmic model. The semisimple and unipotent parts of the monodromy govern, respectively, the power-law and logarithmic growth of flat sections through the tube. Combining this non-Abelian holonomy with the geometric Picard-Lefschetz monodromy yields a decorated cusp label that incorporates Higgs-bundle information and extends tube-wise to intersections of boundary divisors. We also discuss a particular class of monodromy labels for which the weak gauge algebra specified by the fixture and gluing data lies in the reductive monodromy centralizer. In type A, we organize the local monodromy labels into discrete types specified by the eigenspace multiplicities of the semisimple part and the Jordan type of the nilpotent logarithm of the unipotent part. Finally, we illustrate the construction for SL(3,ℂ) on the four-punctured sphere and SL(4,ℂ) on the two-punctured torus.
Related
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BibTeX
@misc{grimm2026asymptotic,
title = {{Asymptotic limits in class-$\mathcalS$ theories and non-Abelian Hodge theory}},
author = {Thomas W. Grimm and Amineh Mohseni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.26883},
eprint = {2609.26883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26883},
}
RIS
TY - UNPB
TI - Asymptotic limits in class-𝒮 theories and non-Abelian Hodge theory
AU - Thomas W. Grimm
AU - Amineh Mohseni
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.26883
UR - https://arxiv.org/abs/2609.26883
AB - We develop a non-Abelian Hodge-theoretic refinement of asymptotic limits in type-A class-𝒮 theories, enriching the geometric description of the degenerating UV curve with gauge-theoretic data encoded by the associated Hitchin system. A degeneration of the UV curve produces a long plumbing tube, which we equip with the local monodromy data of a Hitchin-Simpson flat connection admitting a regular-singular logarithmic model. The semisimple and unipotent parts of the monodromy govern, respectively, the power-law and logarithmic growth of flat sections through the tube. Combining this non-Abelian holonomy with the geometric Picard-Lefschetz monodromy yields a decorated cusp label that incorporates Higgs-bundle information and extends tube-wise to intersections of boundary divisors. We also discuss a particular class of monodromy labels for which the weak gauge algebra specified by the fixture and gluing data lies in the reductive monodromy centralizer. In type A, we organize the local monodromy labels into discrete types specified by the eigenspace multiplicities of the semisimple part and the Jordan type of the nilpotent logarithm of the unipotent part. Finally, we illustrate the construction for SL(3,ℂ) on the four-punctured sphere and SL(4,ℂ) on the two-punctured torus.
ER -