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?

  • $\begingroup$ Whether you demand conformal invariance or not, most QFTs are non-Lagrangian. In any of the CFTs you mentioned, you can break conformal invariance by deforming with a relevant operator times a coupling constant. Do you think they will magically become Lagrangian again no matter how small the coupling is? $\endgroup$ Commented Dec 10, 2021 at 10:46
  • $\begingroup$ @ConnorBehan I think I am getting some inspriation from your answer. Thank you! The only deformation I know is to consider add something like a superpotential with a coupling constant. Is there another methods of deformation you are talking about? $\endgroup$
    – Nugi
    Commented Dec 10, 2021 at 11:19
  • 1
    $\begingroup$ Yeah, superpotentials are the deformations that will preserve at least $\mathcal{N} = 1$ supersymmetry. But there can still be a few different choices for them in arxiv.org/abs/1602.04817 and arxiv.org/abs/1607.04281 for example. Note that these papers are concerned with following the flows all the way to the IR where they lead to CFTs again but this is not necessary. $\endgroup$ Commented Dec 10, 2021 at 11:29
  • $\begingroup$ Thank you very much! $\endgroup$
    – Nugi
    Commented Dec 10, 2021 at 11:46


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