I have been reading about the questions and answers in (Does a non-lagrangian field theory have a stress-energy tensor?) and links in thereof.
My question is the following. Are there non-Lagrangian theories without conformal symmetry?
All the theories coming from the gravity side via AdS/CFT assume that there might be a dual CFT. Are there examples of non-Lagrangian theories without it?
Examples of $\mathcal{N}=3,4$ are conformal as far as I know. Most examples of $\mathcal{N}=2$ non-Lagrangian theories are also conformal.
Can someone shed some light on this?
