• Corpus ID: 211734182

# Open $r$-spin theory II: The analogue of Witten's conjecture for $r$-spin disks

@article{Buryak2018OpenT,
title={Open \$r\$-spin theory II: The analogue of Witten's conjecture for \$r\$-spin disks},
author={Alexandr Buryak and Emily Clader and Ran J. Tessler},
journal={arXiv: Symplectic Geometry},
year={2018}
}
• Published 7 September 2018
• Mathematics
• arXiv: Symplectic Geometry
We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting and a first step toward the construction of an open version of Fan--Jarvis--Ruan--Witten theory. As an unexpected consequence…
14 Citations

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