Conformal field theory, 2014 (Berkeley - math 290)
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 (An and Dn) 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
Time and location: Wednesdays 12:40 -- 2:00pm, in room 736.
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...
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
[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.
[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