Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01028 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917435964129280 |
|---|---|
| author | Kumar, Ayush |
| author_facet | Kumar, Ayush |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01028 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hilbert Series and Complete-Intersection Structure of Coulomb Branches for Non-Maximal Nilpotent Orbits of $SL(N)$ Kumar, Ayush High Energy Physics - Theory 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. |
| title | Hilbert Series and Complete-Intersection Structure of Coulomb Branches for Non-Maximal Nilpotent Orbits of $SL(N)$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.01028 |