D-instanton Effects on a D3-brane

It has been proposed by Sen that the D-instanton effects in string theory can be systematically determined through the framework of open-closed string field theory. We apply the latter formalism to analyze the D-instanton corrections to the quantum effective action of a D3-brane in type IIB superstring theory, and determine the leading single and multi-instanton contributions to the $D^4 F^4$ effective coupling which is unprotected by supersymmetry. Notably, while we find that the one-instanton contribution agrees with a conjecture of Green and Gutperle, the multi-instanton contribution disagrees with the conjecture.