Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids

Details Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids

1999-10-06

arxiv.org/abs/hep-th/9910046v1

Nucl.Phys. B568 (2000) 503-542

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, LaTeX

Scientific paper

10.1016/S0550-3213(99)00738-5

The chiral WZNW symplectic form $\Omega^{\rho}_{chir}$ is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in $\Omega^{\rho}_{chir}$ and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

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