Tropicalization of super Gromov-Witten invariants

Abstract

We show that genus-0, $n$ Neveu-Schwarz marked, super Gromov-Witten invariants of a convex, toric variety $X$ can be defined and computed using tropical geometry. When $X$ is a point, the tropical, super Gromov-Witten invariants of $X$ are descendant invariants on the moduli space of tropical curves. When $X$ is a general convex, toric variety, we define a procedure that computes the tropical, inverse Euler class of the SUSY normal bundle ${\overline{N}}_{n,\beta }\to {\overline{\mathcal{M}}}_{0,n}(X,\beta )$, under the assumption that ${\overline{N}}_{n,\beta }$ is in some sense locally tropicalizable. We define the tropical, genus-0, $n$ Neveu-Schwarz marked, super Gromov-Witten invariants of $X$, and show that the definition recovers the tropical, super Gromov-Witten invariants of a point. We compute a tropical, super Gromov-Witten invariant of ${\mathbb{P}}^1$.

21 pages, exposition improved