Calculable e^{-1/λ} Effects

TL;DR

The paper identifies and computes non-perturbative $e^{-1/\lambda}$ corrections to a class of four-derivative couplings ${\widetilde{\cal F}}_1$ in $D=4$ $N=4$ string theory, using Type II–heterotic duality to map a perturbative one-loop heterotic result to non-perturbative Type II physics on $K3\times T^2$. The exact heterotic computation reveals the leading logarithmic piece and subleading non-perturbative contributions that correspond to Euclidean D-brane instantons, with detailed matching to Type II one-loop results and a clear interpretation in terms of wrapped branes. In the decompactification to ten dimensions, the $R^4$ couplings in Type IIB are shown to be governed by a modular form $f(\rho,\bar{\rho})$, validating conjectured D-instanton contributions and illustrating $SL(2,\mathbb{Z})$ invariance. The work further argues that similar non-perturbative effects should appear in higher ${\widetilde{F}}_g$ and potentially in $N=1$ K"ahler potentials, highlighting the rich structure of hypermultiplet moduli and the power of duality in uncovering non-perturbative dynamics.

Abstract

We identify and evaluate a class of physical amplitudes in four-dimensional N=4 superstring theory, which receive, in the weak coupling limit, contributions of order e^{-1/λ}, where λis the type II superstring coupling constant. They correspond to four-derivative \Ftilde_1 interaction terms involving the universal type II dilaton supermultiplet. The exact result, obtained by means of a one-loop computation in the dual heterotic theory compactified on T^6, is compared with the perturbation theory on the type II side, and the e^{-1/λ} contributions are associated to non-perturbative effects of Euclidean solitons (D-branes) wrapped on K3 x T^2. The ten-dimensional decompactification limit on the type IIB side validates the recent conjecture for the D-instanton-induced R^4 couplings.