# Gauge invariant operators in AdS/CFT

I am working on the AdS/CFT correspondence and I am on the field-operator map. I have found in several textbooks the following statement, which refers to the operators of CFT:

"The field theory operators for which the map is established have to be gauge invariant, which implies that they have to be composite operators."

1) Why these operators must be gauge invariant?

2) Why a gauge invariant operator must be composed by other operators?

• 1) because non-gauge-invariant operators are not well defined (you can write a formula, but it implicitly assumes a choice of a gauge, which is unphysical) 2) this is only true in non-abelian gauge theories, since in an abelian theory $F$ is not composite. Otherwise, the list of fundamental fields is relatively simple and you can try yourself to build gauge-invariants without taking products. – Peter Kravchuk Dec 16 '17 at 18:12