A new spin on polynomial relations among kappa classes

Abstract

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov-Witten theory of the projective line and is dictated by ${\mathbb{Z}}_2$-equivariant topological recursion.

21 pages. v3: proof of Prop. 2.5 rewritten; Remark 2.8 (descendant correlators) added; minor corrections and clarifications