Seminar : Affine Lie Algebras

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

topics

Kac-Moody algebras

chapter 1&4 of [Kac 1994]
chapter 14&15 of [Carter 2005]

affine Lie algebras as central extensions of loop algebras

chapter 7 of [Kac 1994]
chapter 18 of [Carter 2005]

Sugawara construction of Virasoro algebra

chapter 12 of [Kac 1994]
chapter 15 of [FMS 1999]

integrable highest weight representations of affine Lie algebras

chapter 12 of [Kac 1994]
chapter 3 of [Wakimoto 2001]
chapter 20 of [Carter 2005]

Wess-Zumino-Witten model

chapter 15 of [FMS 1999]
Walton, Mark. ‘Affine Kac-Moody Algebras and the Wess-Zumino-Witten Model’. arXiv:hep-th/9911187, 23 November 1999. http://arxiv.org/abs/hep-th/9911187.

modular transformations of characters of affine Lie algebras

chapter 4 of [Wakimoto 2001]
chapter 13 of [Kac 1994]
Macdonald, I. G. 1981. “Affine Lie Algebras and Modular Forms.” In Séminaire Bourbaki Vol. 1980/81 Exposés 561–578, 258–276. Lecture Notes in Mathematics 901. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0097202.

fusion rules and Verlinde formula

chapter 5 of [Wakimoto 2001]
chapter 16 of [FMS 1999]
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. http://arxiv.org/abs/math/0212387
Fuchs, J. 1994. ‘Fusion Rules in Conformal Field Theory’. Fortschritte Der Physik/Progress of Physics 42 (1): 1–48. doi:10.1002/prop.2190420102. http://arxiv.org/abs/hep-th/9306162
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

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 (81 1980): 23–66. doi:10.1007/BF01391662.

links

UQ Quantum Field Theory Seminar 2013-2014

references

[*Kac 1994] Kac, Victor G. 1994. Infinite-Dimensional Lie Algebras. Cambridge University Press.
[*FMS 1999] Francesco, Philippe, Pierre Mathieu, and David Senechal. 1999. Conformal Field Theory. Corrected edition. New York: Springer.
[*Wakimoto 2001] Wakimoto, Minoru. Infinite-Dimensional Lie Algebras. Vol. 195. Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 2001. http://www.ams.org/mathscinet-getitem?mr=1793723.
[*Carter 2005] Carter, R. W. 2005. Lie Algebras of Finite and Affine Type. Vol. 96. Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge. http://www.ams.org/mathscinet-getitem?mr=2188930.

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reading for fun

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. http://www.ams.org/notices/199512/dolan.pdf
Goddard, Peter, and David Olive, eds. Kac-Moody and Virasoro Algebras. Vol. 3. Advanced Series in Mathematical Physics. World Scientific Publishing Co., Singapore, 1988. http://www.ams.org/mathscinet-getitem?mr=966668.