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arXiv · 1809.02536

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

Alexandr Buryak·Emily Clader·Ran J. Tessler
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Abstract

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, we establish a mysterious relationship between open $r$-spin theory and an extension of Witten's closed theory.

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Alexandr Buryak, Emily Clader, Ran J. Tessler. 2018-09-07. Open $r$-spin theory II: The analogue of Witten's conjecture for $r$-spin disks. https://arxiv.org/abs/1809.02536

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