Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories

Understand

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories.

• On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow.
• In this note, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) by performing simple calculations involving sets of non-unitary free four-dimensional hypermultiplets.
• These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow.