Spectral networks, finite webs, and the T3 cubic differential
Abstract
We describe spectral networks for cubic differentials on P1 with exactly three poles all of order two, following observations of Hollands-Neitzke. To do so, we give a precise definition and establish some basic properties of a class of finite webs (corresponding to BPS states in physics) in the cubic differential setting, including their non-vanishing central charge. Turning to the example, we prove that at rational angles the network is totally degenerate; the number of walls and Stokes regions is explicitly computed and depends on an arithmetic criterion. At all other angles, the spectral network is dense in the surface and contains no finite webs, as expected. Physically, this example corresponds to a fundamental building block for a large class of four-dimensional 𝒩=2 QFTs with gauge group SU(3).
Related
- Brauer webs of finite and affine type
- Webs and finite dimensional representation theory for quantum symmetric pairs
- Least energy sign-changing solutions for asymptotically cubic Kirchhoff equations on locally finite graphs
- Spectral gap for the three-dimensional damped cubic wave equation with degenerate noise
- Cubic AGM graphs and Hessian $3$-isogenies over finite fields 𝔽q of odd characteristic with q ≡ 2 pmod3
BibTeX
@misc{kidwai2026spectral,
title = {{Spectral networks, finite webs, and the $T_3$ cubic differential}},
author = {Omar Kidwai and Guillaume Tahar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23752},
eprint = {2610.23752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23752},
}
RIS
TY - UNPB
TI - Spectral networks, finite webs, and the T_3 cubic differential
AU - Omar Kidwai
AU - Guillaume Tahar
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23752
UR - https://arxiv.org/abs/2610.23752
AB - We describe spectral networks for cubic differentials on P^1 with exactly three poles all of order two, following observations of Hollands-Neitzke. To do so, we give a precise definition and establish some basic properties of a class of finite webs (corresponding to BPS states in physics) in the cubic differential setting, including their non-vanishing central charge. Turning to the example, we prove that at rational angles the network is totally degenerate; the number of walls and Stokes regions is explicitly computed and depends on an arithmetic criterion. At all other angles, the spectral network is dense in the surface and contains no finite webs, as expected. Physically, this example corresponds to a fundamental building block for a large class of four-dimensional 𝒩=2 QFTs with gauge group SU(3).
ER -