From strings in 6d to strings in 5d

TL;DR

This paper leverages recent advances in elliptic genus computations for 6d strings to derive elliptic genera for 5d strings, linking physical theories with mathematical sheaf counting on ruled surfaces.

Contribution

It introduces a method to obtain 5d string elliptic genera from 6d results, connecting physical string theories with mathematical sheaf counting.

Findings

Derived explicit formulas for 5d string elliptic genera from 6d results

Established connections between string theory and sheaf counting on ruled surfaces

Extended the applicability of elliptic genus computations across dimensions

Abstract

We show how recent progress in computing elliptic genera of strings in six dimensions can be used to obtain expressions for elliptic genera of strings in five-dimensional field theories which have a six-dimensional parent. We further connect our results to recent mathematical results about sheaf counting on ruled surfaces.