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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01028 |
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Table of Contents:
- We study the Coulomb branches of three-dimensional $\mathcal N=4$ quiver gauge theories of type $T_ρ(SU(N))$ associated with non-maximal nilpotent orbits of $SL(N)$. Using the Hall--Littlewood closed form for Coulomb-branch Hilbert series, together with independent checks from the monopole formula, we compute exact unrefined Hilbert series for all non-maximal partitions $ρ\vdash N$ with $N=4$, and extend the analysis to $N=5,6$. By analyzing the plethystic logarithms of the resulting Hilbert series, we find that in all cases examined the Coulomb branch is a complete intersection. The number of generators and relations follows a uniform pattern governed by the transpose partition $ρ^T$, with exactly $N-1$ relations appearing independently of $ρ$ in these examples. We summarize the results in explicit classification tables and formulate conjectures extending these patterns to arbitrary $N$. Our findings provide strong evidence for a remarkable uniformity in the algebraic structure of Coulomb branches within the $T_ρ(SU(N))$ family at low rank.