Generalized ADHM equations from marginal deformations in open superstring field theory

Abstract

Abstract Working within the framework of both the A ∞ 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 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 back- grounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons.