Hermitian Yang–Mills equations and their generalizations

Abstract

This is a review of the results on Hermitian Yang–Mills equation and their generalization called the deformed Hermitian Yang–Mills equation. Solutions of Hermitian Yang–Mills equation in complex dimension 2 are given by antiself-dual connections so this equation may be considered as a multidimensional generalization of the instanton equations. Deformed Hermitian Yang–Mills equation reduce to the Hermitian Yang–Mills equation in the large volume limit.