Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in 𝒩=4 SYM
Abstract
We study non-minuscule boundary 't Hooft lines in four-dimensional 𝒩=4 U(N) super Yang--Mills theory with the regular Nahm-pole boundary condition. For one-row charges we construct the exact spherical-DAHA operator e+hr(Y)e+, determine its finite shift expansion and discrete Macdonald spectrum, and evaluate the S-dual Neumann Wilson two-line index as a finite-N Macdonald pairing. For the first non-minuscule U(2) coefficient, a local two-minuscule convolution model with Higgs branch T*ℙ1 has two Jeffrey--Kirwan residues, while subtracting the determinant intersection-cohomology summand supplies the additional −t term. The same transverse A1 calculation, dressed by the spectator-root factor, reproduces the first lower U(3) coefficient. The local convolution calculation and its spectator lift provide low-rank checks of the complete DAHA coefficients independent of the inverse recursion, while their boundary-localization interpretation remains conjectural. Assuming an isometric oriented boundary Fourier intertwiner, the DAHA construction is compatible with the expected boundary S-duality relation.
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BibTeX
@misc{li2026sphericaldaha,
title = {{Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in $\mathcal N=4$ SYM}},
author = {Ruiliang Li},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.16660},
eprint = {2606.16660},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16660},
}
RIS
TY - UNPB
TI - Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in 𝒩=4 SYM
AU - Ruiliang Li
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2606.16660
UR - https://arxiv.org/abs/2606.16660
AB - We study non-minuscule boundary 't Hooft lines in four-dimensional 𝒩=4 U(N) super Yang--Mills theory with the regular Nahm-pole boundary condition. For one-row charges we construct the exact spherical-DAHA operator e_+h_r(Y)e_+, determine its finite shift expansion and discrete Macdonald spectrum, and evaluate the S-dual Neumann Wilson two-line index as a finite-N Macdonald pairing. For the first non-minuscule U(2) coefficient, a local two-minuscule convolution model with Higgs branch T^*ℙ^1 has two Jeffrey--Kirwan residues, while subtracting the determinant intersection-cohomology summand supplies the additional −t term. The same transverse A_1 calculation, dressed by the spectator-root factor, reproduces the first lower U(3) coefficient. The local convolution calculation and its spectator lift provide low-rank checks of the complete DAHA coefficients independent of the inverse recursion, while their boundary-localization interpretation remains conjectural. Assuming an isometric oriented boundary Fourier intertwiner, the DAHA construction is compatible with the expected boundary S-duality relation.
ER -