Title of seminar
The Chiral WZNW Phase Space
and its Poisson-Lie Groupoid
Lecturer:
Laszlo FEHER, Univ. Szeged
Outline:
A fascinating aspect of the Wess-Zumino-Novikov-Witten model
is that in addition to its built-in affine Kac-Moody symmetry
it also exhibits certain quantum group properties [1]. There
is a consensus that the classical origin of the quantum group
lies in the Poisson-Lie symmetries of the chiral WZNW phase
space that emerges after splitting the left- and right-moving
degrees of freedom [2]. However, in the definition of the
chiral symplectic structure there appears, unavoidably, a choice
to be made and the resulting Poisson brackets have been previously
analysed only in special cases. In this seminar we describe the
chiral WZNW Poisson brackets in the general case [3], and show
that the Jacobi identity leads to a dynamical generalization of
the classical modified Yang-Baxter equation, which is encoded
in the structure of corresponding Poisson-Lie groupoids.
References:
[1] C. Gomez, M. Ruiz-Altaba and G. Sierra, Quantum Groups in
Two-Dimensional Physics (Cambridge University Press, 1996).
[2] F. Falceto and K. Gawedzki, Lattice Wess-Zumino-Witten model
and quantum groups, J. Geom. Phys. 11 (1993) 251 (hep-th/9209076)
[3] J. Balog, L. Feher and L. Palla, The chiral WZNW phase space
and its Poisson-Lie groupoid, hep-th/9907050.