Dominant Young Diagrams in Matrix Models and Partial Deconfinement

Abstract

We discuss dominant representations (or Young diagrams), in thermal matrix models with gauge symmetry from the perspective of partial deconfinement. We propose a prescription for defining the dominant representations for thermal matrix models with interaction terms. As an explicit example, we consider the large-N Gaussian matrix model. We obtain the Vershik--Kerov--Logan--Shepp (VKLS) shape of the dominant Young diagrams through a new analytic saddle-point analysis based on a mapping of the representation theory of U(∞) to free fermions in two spacetime dimensions. This computation provides a direct derivation of the previously observed functional relation between the shape of the dominant Young diagrams and the eigenvalue distribution of the thermal holonomy: the position of the complex saddle point is naturally identified with the eigenvalue. The dominant Young diagrams admit a natural interpretation in terms of partial deconfinement: the number of rows in the dominant Young diagrams matches the size of the submatrix corresponding to the deconfined subsector.

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BibTeX RIS

BibTeX

@misc{shimada2026dominant,
  title = {{Dominant Young Diagrams in Matrix Models and Partial Deconfinement}},
  author = {Hidehiko Shimada and Hiromasa Watanabe},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13067},
  eprint = {2609.13067},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13067},
}

RIS

TY  - UNPB
TI  - Dominant Young Diagrams in Matrix Models and Partial Deconfinement
AU  - Hidehiko Shimada
AU  - Hiromasa Watanabe
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.13067
UR  - https://arxiv.org/abs/2609.13067
AB  - We discuss dominant representations (or Young diagrams), in thermal matrix models with gauge symmetry from the perspective of partial deconfinement. We propose a prescription for defining the dominant representations for thermal matrix models with interaction terms. As an explicit example, we consider the large-N Gaussian matrix model. We obtain the Vershik--Kerov--Logan--Shepp (VKLS) shape of the dominant Young diagrams through a new analytic saddle-point analysis based on a mapping of the representation theory of U(∞) to free fermions in two spacetime dimensions. This computation provides a direct derivation of the previously observed functional relation between the shape of the dominant Young diagrams and the eigenvalue distribution of the thermal holonomy: the position of the complex saddle point is naturally identified with the eigenvalue. The dominant Young diagrams admit a natural interpretation in terms of partial deconfinement: the number of rows in the dominant Young diagrams matches the size of the submatrix corresponding to the deconfined subsector.
ER  -

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