Power Towers of String Instantons for N=1 Vacua

TL;DR

This paper argues for a novel class of poly-instanton corrections in four-dimensional N=1 string vacua, where instanton actions themselves receive corrections from other instantons, producing an infinite power-tower of non-perturbative contributions to holomorphic couplings. By refining the D-brane instanton calculus and relating zero-mode absorption to holomorphic gauge-threshold data, the authors show how these poly-instanton effects arise and compute explicit multi-instanton amplitudes. They test the framework in a heterotic–Type I S-dual pair based on a freely acting Z2×Z2 orbifold, finding exact matches for single-instanton contributions and revealing additional poly-instanton corrections on the Type I side not captured by the heterotic one-loop sum. The results suggest poly-instanton corrections are generic in N=1 vacua and may have significant implications for moduli stabilization and phenomenology, while remaining consistent with holomorphy and non-renormalization theorems.

Abstract

We provide arguments for the existence of novel hereinafter called poly-instanton corrections to holomorphic couplings in four-dimensional N=1 supersymmetric string compactifications. After refining quantitatively the D-brane instanton calculus for corrections to the gauge kinetic function, we explicitly apply it to the Type I toroidal orbifold defined in arXiv:0710.3080 and compare the results to the proposed heterotic S-dual model. This leads us to the intriguing conclusion that N=1 string vacua feature a power tower like proliferation of instanton corrections.

Figures (7)

• Figure 1: Annulus 1-loop vacuum diagram.
• Figure 2: Möbius strip 1-loop vacuum diagram.
• Figure 3: Annulus diagram for an $E1$-instanton correction to $f_a$. The upper indices give the ghost number of the vertex operators.
• Figure 4: Annulus $D5$-brane diagram with four fermion insertions.
• Figure 5: Position of a single $O(1)$ instanton: This $E1$ wraps the third $T^2$ and is localised on the fixed points $(x_1,y_1)=(0,0)+(1/2,0)$, $(x_2,y_2)=(1/4,0)+(3/4,0)$ of $\Theta$ .