Seminar : Affine Lie Algebras

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This is the page for the seminar on QFT at the University of Queensland. We focus on Affine Lie Algebras for Semester 1, 2015. The main goal is to understand various aspects of the theory of affine Lie algebras in mathematics and physics.

  • when : Thursdays 3-4:30 pm
  • where : Priestly Building Seminar Room 67-442


Some references are given for each topic. But we won't necessarily follow them strictly or cover them all.

introduction (12/3/2015, Chul-hee Lee)

  • overview
  • distribution of the remaining talks

affine Lie algebras as central extensions of loop algebras (19/3/2015, Peter McNamara)

Kac-Moody algebras (2/4/2015, 16/4/2015, Sean Michael Wilson)

Sugawara construction of Virasoro algebra (23/4/2015, Chris Raymond)

integrable highest weight representations of affine Lie algebras (30/4/2015, Inna Lukyanenko)

Wess-Zumino-Witten model (7/5/2015, Nathan McMahon)

  • chapter 15 of [DFMS 1997]
  • Walton, Mark. ‘Affine Kac-Moody Algebras and the Wess-Zumino-Witten Model’. arXiv:hep-th/9911187, 23 November 1999.
  • Goddard, Peter, and David Olive. “Kac-Moody and Virasoro Algebras in Relation to Quantum Physics.” International Journal of Modern Physics A 01, no. 02 (July 1, 1986): 303–414. doi:10.1142/S0217751X86000149.

modular transformations of characters of affine Lie algebras (14/5/2015, 21/5/2015, Alexander Dunn)

fusion rules and Verlinde formula (.)

  • chapter 5 of [Wakimoto 2001]
  • chapter 16 of [DFMS 1997]
  • Gannon, Terry. 2005. “Modular Data: The Algebraic Combinatorics of Conformal Field Theory.” Journal of Algebraic Combinatorics. An International Journal 22 (2): 211–250. doi:10.1007/s10801-005-2514-2.
  • Feingold, Alex J. 2004. ‘Fusion Rules for Affine Kac-Moody Algebras’. In Kac-Moody Lie Algebras and Related Topics, 343:53–96. Contemp. Math. Amer. Math. Soc., Providence, RI.
  • Fuchs, J. 1994. ‘Fusion Rules in Conformal Field Theory’. Fortschritte Der Physik/Progress of Physics 42 (1): 1–48. doi:10.1002/prop.2190420102.
  • Verlinde, Erik. 1988. “Fusion Rules and Modular Transformations in 2D Conformal Field Theory.” Nuclear Physics B 300: 360–376. doi:10.1016/0550-3213(88)90603-7.

vertex operator constructions of basic representations (Masoud Kamgarpour)

  • chapter 14 of [Kac 1994]
  • chapter 20 of [Carter 2005]
  • Frenkel, I. B., and V. G. Kac. “Basic Representations of Affine Lie Algebras and Dual Resonance Models.” Inventiones Mathematicae 62, no. 1 (February 1, 1980): 23–66. doi:10.1007/BF01391662.
  • Lepowsky, James, and Robert Lee Wilson. “Construction of the Affine Lie algebra $A_1^{(1)}$.” Communications in Mathematical Physics 62, no. 1 (1 August 1978): 43–53. doi:10.1007/BF01940329.



reading for fun

  • Helgason, Sigurdur. ‘A Centennial: Wilhelm Killing and the Exceptional Groups’. The Mathematical Intelligencer 12 (3): 54–57. doi:10.1007/BF03024019.
  • Coleman, A. J. ‘The Greatest Mathematical Paper of All Time’. The Mathematical Intelligencer 11 (3): 29–38. doi:10.1007/BF03025189.
  • Berman, Stephen, and Karen Hunger Parshall. ‘Victor Kac and Robert Moody: Their Paths to Kac-Moody Lie Algebras’. The Mathematical Intelligencer 24, no. 1 (13 January 2009): 50–60. doi:10.1007/BF03025312.
  • Dolan, Louise. ‘The Beacon of Kac-Moody Symmetry for Physics’. Notices of the American Mathematical Society 42, no. 12 (1995): 1489–95.
  • O’Raifeartaigh, L. ‘The Intertwining of Affine Kac–moody and Current Algebras’. International Journal of Modern Physics B 13, no. 24n25 (10 October 1999): 3009–20. doi:10.1142/S0217979299002824.

advanced reading