Open -spin theory II: The analogue of Witten's conjecture for -spin disks
arXiv:1809.02536
Abstract
We conclude the construction of -spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open -spin intersection numbers, and we prove that their generating function is closely related to the wave function of the th Gelfand-Dickey integrable hierarchy. This provides an analogue of Witten's -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 -spin theory and an extension of Witten's closed theory.
v5: Comparing to the previous version, v4, the results about open -spin intersection numbers in higher genera were moved to the article arXiv:2211.16302. Accepted for publication in the Journal of Differential Geometry. Comparing to the accepted version, contains Remarks 2.2, 3.6, and 4.9. 63 pages