Topological partition function and string-string duality

TL;DR

This paper provides an exact analytical verification of string-string duality in a specific Calabi-Yau model, extending evidence from vector and gravitational coupling matching, and relates it to the Seiberg/Witten setup.

Contribution

It demonstrates a precise verification of string duality in a rank three example using exact calculations, connecting it to known duality frameworks.

Findings

Confirmed the matching of vector and gravitational couplings in the model

Verified the duality relation through coefficient comparison up to fourth order

Extended the evidence for string/string duality beyond previous checks

Abstract

The evidence for string/string-duality can be extended from the matching of the vector couplings to gravitational couplings. In this note this is shown in the rank three example, the closest stringy analog of the Seiberg/Witten-setup, which is related to the Calabi-Yau $WP^4_{1,1,2,2,6}(12)$. I provide an exact analytical verification of a relation checked by coefficient comparison to fourth order by Kaplunovsky, Louis and Theisen.