Dynamical r matrices and chiral WZNW phase space
Tóm tắt
A dynamical generalization of the classical Yang-Baxter equation that governs the possible Poisson structures on the space of chiral WZNW fields with a generic monodromy is reviewed. It is explained that, for particular choices of chiral WZNW Poisson brackets, this equation reduces to the CDYB equation recently studied by Etingof and Varchenko and by others. Interesting dynamical r matrices are obtained for a generic monodromy, as well as by imposing Dirac constraints on the monodromy.
Tài liệu tham khảo
J.-L. Gervais and A. Neveu, Nucl. Phys. B 238, 125 (1984).
E. Cremmer and J.-L. Gervais, Commun. Math. Phys. 134, 619 (1990).
J. Balog, L. Dabrowski, and L. Fehér, Phys. Lett. B 244, 227 (1990).
G. Felder, hep-th/9407154; in Proceedings of International Congress on Mathematics, Zürich, 1994 (Birkhäuser, Zürich, 1994), p. 1247.
J. Avan, O. Babelon, and E. Billey, Commun. Math. Phys. 178, 281 (1996).
P. Etingof and O. Schiffmann, math.QA/9908064.
P. Etingof and A. Varchenko, Commun. Math. Phys. 192, 77 (1998).
J. Balog, L. Fehér, and L. Palla, Nucl. Phys. B 568, 503 (2000).
E. Witten, Commun. Math. Phys. 92, 455 (1984).
J. Balog, L. Fehér, and L. Palla, hep-th/0007045.
A. Alekseev and Y. Kosmann-Schwarzbach, math.DG/9909176.
K. Gawedzki, Commun. Math. Phys. 139, 201 (1991).
F. Falceto and K. Gawedzki, J. Geom. Phys. 11, 251 (1993).
K. Mackanzie, Lie Groupoids and Lie Algebroids in Differential Geometry (Cambridge Univ. Press, Cambridge, 1987).
A. Weinstein, J. Math. Soc. Jpn. 4, 705 (1988).
A. Alekseev and E. Meinrenken, Invent. Math. 139, 135 (2000).
J. Balog, L. Fehér, and L. Palla, J. Phys. A 33, 945 (2000).