Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$

TL;DR

This paper constructs a quantum curve for the Baker-Akhiezer function associated with the orbifold Gromov-Witten theory of weighted projective lines and derives an explicit fermionic formula for the Gromov-Witten potential.

Contribution

It introduces a quantum curve for the Baker-Akhiezer function and provides a new fermionic formula for the Gromov-Witten potential of orbifold projective lines.

Findings

Quantum curve for orbifold Gromov-Witten theory constructed

Explicit fermionic formula for Gromov-Witten potential derived

Lifting operator from Baker-Akhiezer function formulated

Abstract

We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line $\mathbb P[r]$. Furthermore, we deduce the explicit bilinear Fermionic formula for the (stationary) Gromov-Witten potential via the lifting operator constructed from the Baker-Akhiezer function.