Q-instantons

TL;DR

This paper constructs and analyzes Q-instantons, half-supersymmetric solutions dual to Q7-branes, revealing their role in string theory's non-perturbative effects and their relation to S-duality and higher-order corrections.

Contribution

It introduces Q-instantons described by new fields, expanding the understanding of instanton solutions and their connection to duality symmetries in string theory.

Findings

Q-instantons are dual to Q7-branes and described by fields hi' and T.

They relate to PSL(2,Z) transformations and S-duality.

Q-instantons contribute to higher-order R^4 terms at orbifold points.

Abstract

We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is most conveniently described using the RR axion \chi and the dilaton \phi, the Q-instanton is most conveniently described using a different set of fields \chi' and T, where \chi' is an axionic scalar. The real part of the Q-instanton on-shell action is a function of T and the imaginary part is linear in \chi'. Discrete shifts of the axion \chi' correspond to PSL(2,Z) transformations that are of finite order. These are e.g. pure S-duality transformations relating weak and strongly coupled regimes. We argue that near each orbifold point of the quantum axion-dilaton moduli space PSL(2,Z)\PSL(2,R)/SO(2) the higher order R^4 terms in the string effective action contain contributions from an infinite sum of single multiply-charged instantons with the Q-instantons corresponding to the orbifold points \tau=i,\rho where \tau is the complex axion-dilaton field.