  We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS)
equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS
equations and their connection with the self-dual Yang-Mills equations. Also,
we present a general method allowing to obtain the BPS equations in any
dimension. In addition, we find all BPS equations in the Minkowski space of
dimension $d\leq6$ and apply the obtained results to the supersymmetric
Yang-Mills theories. In conclusion, we discuss the possibility of using the
classification to construct soliton solutions of the low-energy effective
theory of the heterotic string.

High Energy Physics - Theory