Large D-instanton effects in string theory

TL;DR

This paper investigates the large effects of D-instantons in string theory, revealing their asymptotic series nature and proposing that non-perturbative effects like NS5-branes may resolve associated ambiguities.

Contribution

It introduces a Borel resummation approach to analyze the asymptotic D-instanton series and suggests mechanisms to resolve inherent ambiguities in string theory calculations.

Findings

D-instanton series is asymptotic, similar to quantum field theory expansions.

Total D-instanton sum has an ambiguity of order exp(-1/g_s^2).

Including Kaluza-Klein monopoles or NS5-branes can potentially resolve these ambiguities.

Abstract

By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp(-|Q|/g_s)$ to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole micro-states, i.e. of order $\exp(Q^2)$. The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a Calabi-Yau threefold. In either case, the D-instanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Borel-type resummation method, adapted to the Gaussian growth of the D-instanton series, we find that the total D-instanton sum has an inherent ambiguity of order $\exp(-1/g_s^2)$. We further suggest that this ambiguity can be lifted by including Kaluza-Klein monopole or NS5-brane instantons.