Conformal properties of soft operators -- 2 : Use of null-states

Understand

Representations of the (Lorentz) conformal group with the soft operators as highest weight vectors have two universal properties, which we clearly state in this paper.

• Given a soft operator with a certain dimension and spin, the first property is about the existence of "(large) gauge transformation" that acts on the soft operator.
• The second property is the decoupling of (large) gauge-invariant null-states of the soft operators from the $S$-matrix elements.
• In each case, the decoupling equation has the form of zero field-strength condition with the soft operator as the (gauge) potential.