Geodesic
The Poisson--Lie $T$-Duality and Zero Modes
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 462-476

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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. 
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     author = {S. Klimchik and S. E. Parkhomenko},
     title = {The {Poisson--Lie} $T${-Duality} and {Zero} {Modes}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {462--476},
     publisher = {mathdoc},
     volume = {139},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a7/}
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S. Klimchik; S. E. Parkhomenko. The Poisson--Lie $T$-Duality and Zero Modes. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 462-476. http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a7/