This article is cited in 3 papers

The Poisson–Lie $T$-Duality and Zero Modes

S. Klimchik^a, S. E. Parkhomenko<sup>ba

a</sup> Institut de Mathématiques de Luminy
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We consider the Lu–Weinstein–Soibelman Drinfeld double $D$ and a pair of $\sigma$-models associated with it. We show that the Poisson–Lie T-duality relating them can be extended to include string configurations with a nonunit non-Abelian momentum. The dual string configuration (living on the maximal compact subgroup of $D$) then develops a nontrivial monodromy taking values in the Weyl alcove. We also give the duality-invariant action of this dynamical system and describe the analogous phenomenon for the dressing cosets.

Keywords: strings, $\sigma $-model, $T$-duality.

Received: 27.02.2003

DOI: 10.4213/tmf66

 English version: Theoretical and Mathematical Physics, 2004, 139:3, 834–845

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