About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane

The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in

JHEP {\bf 10} (2005) 071

, where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can be also constructed by means of the noncommutative extension of the uniton method proposed in

JHEP {\bf 0408} (2004) 054

by Ki-Myeong Lee. Particularly some specific solutions of the nc Liouville model are explicit constructed.

Note:

24 pages Journal-ref: J. Phys. A: Math. Gen. 39 (2006) 5979-5994 DOI: 10.1088/0305-4470/39/20/023

11.10.Nx
field theory: conformal
field theory: Toda
dimension: 2
Wess-Zumino-Witten model
Chern-Simons term
duality
differential geometry: noncommutative

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