Time and Place
Room 428, Geomatikum, 18:00 on Tuesdays weekly.
Schedule (Feel free to volunteer for any of the talks)
0. Oct 15: Organisation
1. Oct 22: Conformal transformation [S] Chapter 1 ( Sridhar Hariharakrishnan) Notes
2. Oct 29: Conformal group [S] Chapter 2 (Dang Dang) Notes
3. Nov 5: Virasoro algebra [S] Chapter 5 (Karolis Dembickas) Notes
4. Nov 12: Representation Theory of Virasoro algebra [S] Chapter 6 (Bangxin Wang) Notes
5. Nov 19: Wightman axioms [S] Chapter 8.1-8.3 (Sridhar Hariharakrishnan) Notes
6. Nov 26: Wightman axioms (cont) [S] Chapter 8.4-8.6 (Karolis Dembickas) Notes
7. Dec 3: Wightman 2-D QFT with conformal symmetry [S] Chapter 8.7, 9 .1-9.2 (Dang Dang) Notes
8. Dec 10: Wightman 2-D QFT with conformal symmetry continued [S] Chapter 9 .3-9.4 -and [K] Chapter 1.1-1.2 (Dang Dang) Notes
9. Dec 17: Definition of Vertex algebra and formal distributions [K] Chapter 1.3-1.4, 2.1-2.3 (Bangxin Wang) Notes
10. Jan 7: More on locality and current, Virasoro algebra [K] Chapter 2.4-2.6 (Kostya Tolmachov) Notes
11. Jan 14: Operator product expansion (OPE) and Wick’s theorem [K] Chapter 3.1-3.3 (Sridhar Hariharakrishnan) Notes
12. Jan 21: Free boson/fermion vertex algebras [K] Chapter 3.5-3.6 (Karolis Dembickas) Notes
13. Jan 28: ”Reconstruction” theorem for vertex algebras [K] Chapter 4.1-4.6 (Dang Dang)
References
Conforomal Field Theory
Main reference: Martin Schottenloher, A Mathematical Introduction into Conformal Field Theory, 2nd edition [S]: Self-contained introduction to the mathematics tools used in CFT.
Other helpful references:
1. Plauschinn, Blumenhagen, Introduction to Conformal Field Theory: With Applications to String Theory: Chapter 1 is pretty much the same as [S] but using physics notation and has more computations/examples.
2. Pavel Mnev, Lecture notes on Conformal Field Theory: A much more demanding mathematical introduction to CFT with a section on CS-WZW correspondence.
Vertex Operator Algebra
Main reference: Victor Kac, Vertex algebras for beginners [K]: Concise introduction to vertex algebras and often provides physical motivations.
Other helpful references:
1. Frenkel, Ben-Zvi, Vertex Algebras and Algebraic Curves: More detailed and geared towards algebro-geometric point of view, has a lot of material.
2. J. Lepowsky and H. Li, Introduction to Vertex Operator Algebras and Their Representations: Has a lot of details on representation of VOAs associated to Lie algebras (Heisenberg, Virasoro, Kac-Moody) and lattice VOA.
Prerequisites:
1. Basic notions in differential geometry, complex/functional analysis (Tangent space, Cauchy integral, Fourier series,...).
2. First course in Lie group/algebra and representation (PBW basis, Verma modules, induced rep, triangular decomposition,...).
3. Basics on cohomology and central extension of Lie algebras (Reviewed in [S] Chapters 3 and 4).
4. No physics background will be assumed, though it will be helpful.