# Question about BPS solitions

From what I've read earlier, the definition of a BPS soliton is a soliton satisfying a Bogomolny bound (mass bounded from below). Now, I have encountered another definition, which says that a BPS soliton is a soliton preserving (at least some) supersymmetry. I don't really understand the connection between these two definitions. An explanation of this matter would be much appreciated!

Thanks in advance!

## Answers and Replies

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From what I've read earlier, the definition of a BPS soliton is a soliton satisfying a Bogomolny bound (mass bounded from below). Now, I have encountered another definition, which says that a BPS soliton is a soliton preserving (at least some) supersymmetry. I don't really understand the connection between these two definitions. An explanation of this matter would be much appreciated!

Thanks in advance!
The Bogomolny bound is independent from supersymmetry. It describes a minimum energy solution of the classical field equations. However, there is a priori no reason why it should hold when quantum corrections are included.

This is where supersymmetry comes to the rescure: if the solution preserves some supersymmetry, then there are no such quantum corerections and the Bogomolny bound is true also in the full quantum theory. This fact allows to make exact non-perturbative statements in supersymmetric gauge and string theories (which would be almost impossible to make in theories without supersymmetry).