Higher Derivative Couplings and Heterotic-Type I Duality in Eight Dimensions

TL;DR

This paper computes higher derivative couplings in eight-dimensional heterotic and type I string theories, revealing dualities and enumerative geometry connections, with explicit formulas and verification of perturbative and non-perturbative contributions.

Contribution

It provides explicit formulas for F^4 and R^4 couplings, demonstrating duality consistency and linking string couplings to genus g curve counting on K3 surfaces.

Findings

Holomorphic coupling F_g expressed as polylogarithm, counting genus g curves.

Verification of heterotic one-loop couplings matching open and D-string contributions.

Derived closed-form expressions for world-sheet tau-integrals with multiple insertions.

Abstract

We calculate F^4 and R^4T^(4g-4) couplings in d=8 heterotic and type I string vacua (with gauge and graviphoton field strengths F,T, and Riemann curvature R). The holomorphic piece F_g of the heterotic one-loop coupling R^4T^(4g-4) is given by a polylogarithm of index 5-4g and encodes the counting of genus g curves with g nodes on the K3 of the dual F-theory side. We present closed expressions for world-sheet tau-integrals with an arbitrary number of lattice vector insertions. Furthermore we verify that the corresponding heterotic one-loop couplings sum up perturbative open string and non-perturbative D-string contributions on the type I side. Finally we discuss a type I one-loop correction to the R^2 term.