Bertrand Eynard - Considerations about Resurgence Properties of Topological Recursion
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 15/06/2019

To  a  spectral  curve  $S$  (e.g.  a  plane  curve  with  some  extra  structure), topological recursion associates a sequence of invariants: some numbers $F_g(S)$ and some  $n$-forms  $W_{g,n}(S)$.  First  we  show  that  $F_g(S)$  grow  at most  factorially  at large  $g$,  $F_g  =  O((\beta  g)!  r^{-g})$with  $r superior at 0$  and  $\beta\leq  5$.This  implies  that there is a Borel transform of $\sum_g \hbar^{2g-2} F_g$ that is analytic in a disk of radius $r$. The question is whether this is a resurgent series or not?We  give  arguments  for  this,  and  conjecture  what  are  the  singularities  of  the  Borel transform, and we show how it works on a number of examples.