Prepotentials from Symmetric Products

TL;DR

This paper explores the computation of F^4 couplings in 8D string compactifications using differential equations linked to the geometry of symmetric products of K3 surfaces, supporting a five-fold geometric conjecture.

Contribution

It demonstrates how to derive the prepotential from inhomogeneous differential equations resembling Picard-Fuchs equations for Sym^2(K3) fibrations.

Findings

Prepotentials can be obtained from solutions to specific differential equations.

The differential equations are related to the geometry of Sym^2(K3) over P^1.

Evidence supports the conjecture of a five-fold geometric structure underlying these couplings.

Abstract

We investigate the prepotential that describes certain F^4 couplings in eight dimensional string compactifications, and show how they can be computed from the solutions of inhomogenous differential equations. These appear to have the form of the Picard-Fuchs equations of a fibration of Sym^2(K3) over P^1. Our findings give support to the conjecture that the relevant geometry which underlies these couplings is given by a five-fold.