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I am looking for introductory lecture notes or a textbook on conformal nets. It should be as self-contained as possible. I am particularly interested in learning about sectors. Preferably it would have examples of conformal nets, other than the ones associated to loop groups and vertex operator algebras. I believe one can construct a conformal net using the Clifford algebra associated to the Hilbert space $L^{2}(S^{1},\mathbb{C})$, a source where this example is treated in some way would be best.

I am aware of the lecture notes by Yasuyuki Kawahigashi, but they are far from self-contained.

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André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).

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    $\begingroup$ Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer. $\endgroup$ – Peter Oct 13 '17 at 13:38
  • $\begingroup$ @Peter You're welcome! I hope you're enjoying Germany :) $\endgroup$ – Jules Lamers Oct 14 '17 at 12:43
  • $\begingroup$ @Peter PS. A next time I would recommend MathOverflow for these kind of questions $\endgroup$ – Jules Lamers Oct 31 '17 at 19:56
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In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.

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