Conformal field theory, 2014  (Berkeley - math 290)

Description: This course is an introduction to constructive conformal field theory in two dimensions. I will focus exclusively on the so-called "SU(2) conformal field theories". These are the simplest non-abelian conformal field theories, and they admit a beautiful classification in two infinite families (A_n and D_n) and three exceptional cases (E₆, E₇, E₈).
The formalism that I will be using is that of Haag and Kastler, where a quantum field theory is taken to be functor that assigns to every open subset of "space-time" (taken here to be S¹ × ℝ, with its standard metric of indefinite signature) a von Neumann algebra of so-called "local observables".
Prerequisites: A solid understanding of Hilbert spaces. Basic knowledge of the Lie group SU(2), its Lie algebra su(2), and their representation theory.
Time and location: Wednesdays 12:40 -- 2:00pm, in room 736.

Course notes
Post script:
In this class, I ended up covering much much less than I had hoped to. I wanted to at least discuss the fusion rules of the SU(2) chiral WZW model, but didn't even get the chance to define the fusion product...

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The course will be complemented by a seminar (Mondays 16:00 -- 17:30 more like 16:25 -- 17:50):
Location: The ''Baker Board Room'' on the 1st floor of MSRI. To get there, tame the 4:10pm campus bus "HILL" that departs in front of Evans Hall and/or in front of the Hearst Mining Building. MSRI is the very last stop of this bus, and then you still need to walk 50 meters (downhill).

• Wightman axioms and Haag Kastler axioms (Zachary Stone, Monday 24/2)
[Araki]: Sections 4.1, 4.8, 4.9; [Haag]: Sections II.1.2, III.1(with out the stuff about unobservable fields), III.4; [Stasz] Section 2.2.
• Free fields (Daniel Brügmann, Monday 3/3)
[Araki]: 3.5 and appendix C; [BFV]: Section 2.3;
--(mind the gap)--
• Conformal nets (=chiral CFT): some examples (2×) (Shan Shah Monday 24/3 + Jamer Tener Monday 31/3)
[GF] Section III; [Bi] Sections 3.4 and 3.5; additional references: [BMT], [Stasz], [Dong-Xu].
• Superselection theory (=representations) (Dave Penneys)
[GF], [Mü] Section 2.2, [Haag] IV.2


References:
[Araki]: Mathematical theory of quantum fields. Amazon
[Bi] Bischoff, Marcel: Models in boundary quantum field theory associated with lattices and loop group models. ArXiv
[BFV] Brunetti, Fredenhagen, Verch: The generally covariant locality principle - A new paradigm for local quantum field theory. arXiv
[BMT] Buchholz, Mack, Todorov: The current algebra on the circle as a germ of local field theories. Elsevier
[Dong-Xu] Conformal nets associated to lattices and their orbifolds. arXiv
[GF] Gabbiani, Frölich: Operator algebras and conformal field theory. Euclid
[Haag]: Local quantum Physics: Fields, particles, algebras. Amazon
[Mü]: Michael Müger: On the structure and representation theory of rational chiral conformal theories. notes
[Stasz]: Die lokale Struktur abelscher Stromalgebren auf dem Kreis. PhD thesis