mp.mathematical physics – Intuition for conformal nets

I was planning on reading the work of Arthur Bartels, Christopher L. Douglas and André Henriques on the 3-category of conformal nets as discussed in these papers: Coordinate-free nets, Conformal blocks, Fusion of defects, The 3-category and Dualizability.

I wanted to know how the structure of a conformal net arises from the physical notion of a conformal field theory.