On the integrable structure of the Wess-Zumino-Novikov-Witten model
par
Fokko du Cloux
Bat. Braconnier
The Wess-Zumino-Novikov-Witten model is a conformal field theory depending on the choice of a simple Lie group and built from the associated affine Kac-Moody algebra. The latter is an infinite-dimensional Lie algebra, describing the commutation relations of the theory’s fundamental fields. In this talk, I will discuss various results and conjectures on the integrable structure of this model, focusing on the group SU(2) for simplicity. This integrable structure consists of an infinite number of commuting operators in the (completed) universal enveloping algebra of the affine algebra. In the second part of the talk, I will discuss the diagonalisation of these operators on Verma modules of the affine algebra. In particular, I will formulate a conjectural description of their spectrum in terms of well chosen ordinary differential equations, motivated by an affinisation of the geometric Langlands correspondence.
Johannes Kellendonk, Alexander Thomas