Constructing the Monopole Formula for A-Type Good Quivers via Quiver Yangians

@misc{chen2026constructing,
  title = {{Constructing the Monopole Formula for $A$-Type Good Quivers via Quiver Yangians}},
  author = {Tiantai Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06711},
  eprint = {2609.06711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06711},
}

TY  - UNPB
TI  - Constructing the Monopole Formula for A-Type Good Quivers via Quiver Yangians
AU  - Tiantai Chen
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06711
UR  - https://arxiv.org/abs/2609.06711
AB  - Based on the conjectured (and checked for tree-type quivers) quiver Yangian/Coulomb branch algebra correspondence, we give a quiver Yangian interpretation of the monopole formulas for 3D 𝒩=4 good A-type quiver gauge theories, also known as the T_ρ(SU(N)) theories. Using the algebra action on the 1/2-BPS vortices, we reorganize the generators of the truncated shifted quiver Yangian into boundary-adapted generators, and obtain the classical relations in terms of U(N) Casimirs on the Slodowy slice 𝒮^gl_N_ρ, whose coordinates are given by these boundary-adapted generators. We also show that the boundary-adapted generators and the Casimir relations have the correct fugacities as predicted by the Hall-Littlewood expression of the monopole formula for T_ρ(SU(N)), hence reconstructing it as the Hilbert series of the truncated shifted quiver Yangian.
ER  -