Summing up Open String Instantons and N=1 String Amplitudes

TL;DR

This paper calculates instanton expansions of holomorphic couplings in certain N=1 open string vacua, linking them to topological string amplitudes and BPS domain wall counts, and also explores genus one partition functions in Calabi-Yau 4-folds.

Contribution

It provides explicit instanton expansion computations for holomorphic couplings in N=1 open string theories and relates these to topological string amplitudes and BPS domain wall counting.

Findings

Holomorphic couplings match BPS domain wall counting functions.

Computed genus one partition function for topological strings on Calabi-Yau 4-folds.

Confirmed agreement with theoretical interpretations of open string instantons.

Abstract

We compute the instanton expansions of the holomorphic couplings in the effective action of certain $\cx N=1$ supersymmetric four-dimensional open string vacua. These include the superpotential $W(\phi)$, the gauge kinetic function $f(\phi)$ and a series of other holomorphic couplings which are known to be related to amplitudes of topological open strings at higher world-sheet topologies. The results are in full agreement with the interpretation of the holomorphic couplings as counting functions of BPS domain walls. Similar techniques are used to compute genus one partition function for the closed topological string on Calabi--Yau 4-fold which gives rise to a theory with the same number of supercharges in two dimensions.