Closed extended $r$spin theory and the GelfandDickey wave function
Abstract
We study a generalization of genuszero $r$spin theory in which exactly one insertion has a negativeone twist, which we refer to as the "closed extended" theory, and which is closely related to the open $r$spin theory of Riemann surfaces with boundary. We prove that the generating function of genuszero closed extended intersection numbers coincides with the genuszero part of a special solution to the system of differential equations for the wave function of the $r$th GelfandDickey hierarchy. This parallels an analogous result for the open $r$spin generating function in the companion paper to this work.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 DOI:
 10.48550/arXiv.1710.04829
 arXiv:
 arXiv:1710.04829
 Bibcode:
 2017arXiv171004829B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics
 EPrint:
 v3: 25 pages, minor corrections according to referee's remarks