Nonlinear Instantons from Supersymmetric p-Branes

TL;DR

This paper derives nonlinear deformations of instanton equations for supersymmetric D-branes with gauge fields and B-fields, connecting them to noncommutative geometry and M5-brane configurations in Calabi-Yau spaces.

Contribution

It introduces nonlinear instanton equations for D-branes with gauge fields in B-field backgrounds and relates M5-brane instantons to Kodaira-Spencer equations, expanding the understanding of supersymmetric brane configurations.

Findings

Deformed instanton equations depend on B-field, geometry, and cycle data.

Connections established between deformed instantons and noncommutative geometry.

M5-brane instantons relate to Kodaira-Spencer equations.

Abstract

Supersymmetric configurations of type II D-branes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the kappa-symmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the B-field, the background geometry and the cycle wrapped by the brane. In the appropriate dimensions, limits and settings these equations reduce to deformed instanton equations recently found in the context of noncommutative geometry as well as those following from Lagrangians based on Bott-Chern forms. We further consider instantons comprised of M5-branes wrapping a Calabi-Yau space with non-vanishing three-form field strengths. It is shown that the instanton equations for the three-form are related to the Kodaira-Spencer equations.