Generalized ADHM equations from marginal deformations in open superstring field theory

TL;DR

This paper derives conditions for exact marginal deformations in open superstring field theory, leading to generalized ADHM equations, and confirms the stability of certain instanton moduli up to third order.

Contribution

It provides a new computational approach to derive algebraic constraints for marginal deformations in superstring field theory, extending the ADHM framework.

Findings

Derived a necessary and sufficient condition for marginal deformations to be exact up to third order.

Localized the condition on the boundary of the worldsheet moduli space for specific backgrounds.

Confirmed the stability of the D(-1)/D3 instanton size modulus up to third order.

Abstract

Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the $\mathrm{D(-1)/D3}$ system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory. We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons.