Instanton amplitudes in open-closed topological string theory

TL;DR

This paper develops a universal instanton formalism to analyze quantum effects and instanton corrections in open-closed topological string theory on Calabi-Yau manifolds with multiply-wrapped D-branes, providing new insights into amplitude corrections and non-renormalization theorems.

Contribution

It introduces a formalism that precisely defines instanton corrections in open-closed topological strings with multiply-wrapped D-branes, extending previous homological approaches and proving non-renormalization theorems.

Findings

Provides a geometric non-renormalization proof for certain amplitudes.

Clarifies the role of instanton corrections in boundary BRST operators.

Offers a framework for understanding instanton effects beyond the singly-wrapped case.

Abstract

I use the universal instanton formalism to discuss quantum effects in the open-closed topological string theory of a Calabi-Yau A-model, in the presence of a multiply-wrapped `Floer' D-brane. This gives a precise meaning (up to the issue of compactifying the relevant moduli spaces) to the instanton corrections which affect sigma model and topological string amplitudes. The cohomological formalism I use recovers the homological approach used by Fukaya and collaborators in the singly-wrapped case, even though it is not a naive generalization of the latter. I also prove some non-renormalization theorems for amplitudes with low number of insertions. The non-renormalization argument is purely geometric and based on the universal instanton formulation, and thus it does not assume that the background satisfies the string equations of motion. These results are valid even though the D-brane background typically receives worldsheet instanton corrections. I also point out that the localized form of the boundary BRST operator receives instanton corrections and make a few comments on the consequences of this effect.