Exact Thresholds and Instanton Effects in String Theory

TL;DR

This paper explores instanton effects in string theories with 16 supersymmetries, analyzing dualities, perturbative tests, and various non-perturbative instanton contributions across different dimensions.

Contribution

It provides a detailed analysis of instanton effects and duality tests in string theories with 16 supersymmetries, including new insights into non-perturbative phenomena.

Findings

Matching heterotic one-loop and type II tree-level amplitudes confirms duality.

Identification of D-brane and NS5-brane instantons in specific compactifications.

Revelation of Kaluza-Klein 5-brane instanton effects in three-dimensional theories.

Abstract

In this lecture we summarize some recent work on the understanding of instanton effects in string theories with 16 supersymmetries. In particular, we consider F^4 couplings using the duality between the heterotic string on T^4 and type IIA on K_3 at an orbifold point, as well as higher and lower dimensional versions of this string-string duality. At the perturbative level a non-trivial test of the duality, requiring several miraculous identities, is presented by matching a purely one-loop heterotic amplitude to a purely tree-level type II result. A wide variety of non-perturbative effects is shown to occur in this setting, including D-brane instantons for type IIA on K_3 x S^1 and NS5-brane instantons for type IIA on K_3 x T^2. Moreover, the analysis of the three-dimensional case, which possesses a non-perturbative SO(8,24,Z) U-duality, reveals the presence of Kaluza-Klein 5-brane instanton effects, both on the heterotic and the type II side.