I assume you know that free field theories can be constructed (in arbitrary dimension of spacetime, I believe).
In algebraic quantum field theory (a la Haag), there is for example the conformal Ising model. You can find more about this in these references:
- Mack, G., & Schomerus, V. (1990). Conformal field algebras with quantum symmetry from the theory of superselection sectors. Communications in Mathematical Physics, 134(1), 139–196.
- Böckenhauer, J. (1996). Localized endomorphisms of the chiral Ising model. Communications in Mathematical Physics, 177(2), 265–304.
In the latter "localized endomorphisms" as in the Doplicher-Haag-Roberts programme on superselection sectors. See for example this paper on the arXiv.
There are surely more examples, also in the Wightman setting, but I'm not too familiar with them.
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