Topological String Partition Functions as Polynomials

TL;DR

This paper demonstrates that higher genus topological string partition functions on the quintic can be expressed as polynomials of five generators, providing explicit forms for several genera and coefficients.

Contribution

It introduces a polynomial structure for higher genus partition functions and computes explicit forms for genus 2, 3, and 4.

Findings

Partition functions are polynomials of five generators.

Explicit polynomial forms for genus 2, 3, and 4 are derived.

Coefficients are provided for all genus.

Abstract

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.