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Free Field Realizations in Representation Theory and Conformal Field Theory

In: Proceedings of the International Congress of Mathematicians

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  • Edward Frenkel

    (Harvard University, Department of Mathematics)

Abstract

Free field realization is a relatively new formalism that intertwines representation theory, conformal field theory, and the theory of nonlinear integrable equations. From the physics point of view, it provides realizations of two-dimensional conformal field theories via free bosonic theories. This allows one to find integrals of motion and compute explicitly correlation functions. Mathematically, free field realizations bring new insights into representation theory of conformal algebras, e.g., a new series of representations of affine Kac-Moody algebras, which can be considered as an analogue of the principal series of semi-simple groups over local fields. This connects representation theory of affine algebras with Langlands philosophy.

Suggested Citation

  • Edward Frenkel, 1995. "Free Field Realizations in Representation Theory and Conformal Field Theory," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 1256-1269, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_120
    DOI: 10.1007/978-3-0348-9078-6_120
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