Exact thresholds and instanton effects in D=3 string theories

TL;DR

This paper derives an exact non-perturbative expression for a specific amplitude in three-dimensional string theories with 16 supersymmetries, revealing instanton effects and new contributions unique to three dimensions.

Contribution

It proposes a covariantized U-duality invariant amplitude that captures all perturbative and non-perturbative effects, including novel instanton contributions in D=3 string theories.

Findings

Exact expression for the $( abla )^4$ amplitude in D=3 string theories.

Identification of new instanton contributions, including Kaluza-Klein 5-branes.

Extraction of the summation measure for these instanton effects.

Abstract

Three-dimensional string theories with 16 supersymmetries are believed to possess a non-perturbative U-duality symmetry $SO(8,24,\Zint)$. By covariantizing the heterotic one-loop amplitude under U-duality, we propose an exact expression for the $(\partial \phi)^4$ amplitude, that reproduces known perturbative limits. The weak-coupling expansion in either of the heterotic, type II or type I descriptions exhibits the well-known instanton effects, plus new contributions peculiar to three-dimensional theories, including the Kaluza-Klein 5-brane, for which we extract the summation measure. This letter is a post-scriptum to hepth/0001083.