Fivebranes, Membranes and Non-Perturbative String Theory

TL;DR

This paper investigates non-perturbative corrections in type IIA string theory compactified on Calabi-Yau spaces, revealing contributions from instantons involving strings, membranes, and fivebranes, and relating them via quantum mirror symmetry.

Contribution

It introduces a unified framework for calculating instanton corrections involving multiple brane types and establishes their relation through quantum mirror symmetry.

Findings

Derivation of instanton corrections with order e^{-1/g_s} contributions.

Identification of supersymmetric cycles as those with vanishing pullback of the Kähler form.

Establishment of quantum mirror symmetry relating cycles in IIA and IIB theories.

Abstract

Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g_s$ is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the Calabi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the K\"ahler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odd-dimensional cycles in the Calabi-Yau space to a sum in the IIB theory over supersymmetric, even-dimensional cycles in the mirror.