Seminar topics on affine Lie algebras

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

Meetings: Thursdays 3-4:30 pm, Priestly Building Seminar Room 67-442


topics

Kac-Moody algebras

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

affine Lie algerbas as central extensions of loop algerbas

  • 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.


future topics

  • admissible representations
  • Heisenberg or Virasoro?

memo


links


references

<HarvardReferences>

  • [*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.

</HarvardReferences>


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.


invitation

INVITATION EMAIL SENT TO EVERYBODY IN MATH AND PHYSICS

Dear colleagues,

We are having a seminar on Affine Lie Algebras this semester. The goal is to understand various aspects of the theory useful in both mathematics and physics. The seminar will meet once a week on

Thursdays 3:00-4:30 pm - Priestly Building 67-442. The first meeting will be this coming Thursday (March 1).

This is a continuation of the seminar we had last semester regarding mathematical aspects of quantum field theory. Following the approach of the last semester, most of the talks will be given by students and on voluntary basis. The talks will be of informal nature, with lots of questions and discussions. New postgraduate students who are interested in the topic are especially encouraged to participate. We hope to continue to have the presence of the more knowledgable staff to guide us through the intricacies of the subject.

The program of the seminar can be found at: https://sites.google.com/site/masoudkomi/research/qft

This is the only email sent to the mass email list regarding this semester's seminar. If you are not already on the seminar's list and would like to be informed, please send me an email and I will include you in the future announcements.

All the best,

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