Primary field

In theoretical physics, a primary field is a field operator in quantum field theory - especially conformal field theory or a theory with supersymmetry - that is invariant under the positive frequency modes of the Virasoro algebra - or under one half of the supersymmetries and superconformal generators.

In conformal field theory, a primary field is equivalent to a tensor field with well-defined weights and simple operator product expansion with the stress-energy tensor. In the state-operator correspondence, a primary field is associated with a highest-weight vector. One can also discuss quasi-primary fields, which transform as tensor representations of the global conformal group (as opposed to primary fields, which vary under local conformal transformations).

A descendant field or a secondary field is, on the contrary, a field that is not primary but a field that can be written as the action of negative frequency modes of the Virasoro algebra on a primary field. In terms of representation theory, each irreducible representation contains one primary field and many descendant fields.

See also

• Vertex algebra
• Knizhnik–Zamolodchikov equations
• Fusion rule