Bogomol'nyi–Prasad–Sommerfield bound

In the classical bosonic sector of a supersymmetric field theory, the Bogomol'nyi–Prasad–Sommerfield (BPS) bound (named after Evgeny Bogomolny, M.K. Prasad, and Charles Sommerfield) provides a lower limit on the energy of static field configurations, depending on their topological charges or boundary conditions at spatial infinity. This bound manifests as a series of inequalities for solutions of the classical bosonic field equations. Saturating this bound, meaning the energy of the configuration equals the bound, leads to a simplified set of first-order partial differential equations known as the Bogomolny equations. Classical solutions that saturate the BPS bound are called "BPS states". These BPS states are not only important solutions within the classical bosonic theory but also play a crucial role in the full quantum supersymmetric theory, often corresponding to stable, non-perturbative states in both field theory and string theory. Their existence and properties are deeply connected to the underlying supersymmetry of the theory, even though the bound itself can be formulated within the bosonic sector alone.

In theoretical physics, specifically in theories with extended supersymmetry, the BPS bound is a lower limit on the mass of a physical state in terms of its charges. States that saturate this bound are known as BPS states, and they have special properties, such as being invariant under some fraction of the supersymmetry transformations. The acronym BPS stands for Bogomol'nyi, Prasad, and Sommerfield, who first derived the bound in the context of magnetic monopoles in Yang-Mills theory in 1975.