Heterotic/Type-I Duality in D<10 Dimensions, Threshold Corrections and D-Instantons

TL;DR

This paper explores heterotic/type-I duality in lower dimensions, calculating BPS saturated terms and D-instanton effects, revealing a deep connection between perturbative and non-perturbative contributions in string theory.

Contribution

It provides a novel prescription for D-instanton calculations in type I string theory using heterotic duality, including the role of elliptic genera and matrix model interpretations.

Findings

Heterotic and type-I theories' BPS terms match in lower dimensions.

D1-instanton determinants relate to elliptic genera evaluated at complex structures.

Perturbative thresholds agree with D-instanton calculations across dimensions.

Abstract

We continue our study of heterotic/type-I duality in D<10 dimensions. We consider the heterotic and type-I theories compactified on tori to lower dimensions. We calculate the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action. These terms are expected to be non-perturbatively exact for D>4. The heterotic result is compared with the associated type-I result. In D<9 dimensions, the type-I theory has instanton corrections due to D1 instantons. In D=8 we use heterotic-type I duality to give a simple prescription of the D-instanton calculation on the type I side. We allow arbitrary Wilson lines and show that the D1-instanton determinant is the affine character-valued elliptic genus evaluated at the induced complex structure of the D1-brane world-volume. The instanton result has an expansion in terms of Hecke operators that suggest an interpretation in terms of an SO(N) matrix model of the D1-brane. The total result can be written in terms of generalized prepotentials revealing an underlying holomorphic structure. In D<8 we calculate again the heterotic perturbative thresholds and show that they agree with the D1-instanton calculation using the rules derived in D=8.