In theoretical physics, the Sugawara theory is a set of formulae and theorems that allow one to construct a stress-energy tensor of a specific type of conformal field theory from a bilinear expression involving currents.

How to interpret the Sugawara construction from a physical or mathematical viewpoint?

Sugawara construction is a kind of method to embed Virasoro algebra into completions of universal enveloping algebras of affine algebras ? what special properties do this kind of embedding have? In soliton theory, I know there is a boson-fermion correspondence which realize free boson algebra in the completion of free fermion algebra.
I wonder if there are some common principles under them?