Noncommutative Integrable Field Theories in 2d

Abstract

We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its na\"ıve noncommutative generalization is {\em not} integrable. On the other hand, the addition of extra constraints, obtained through the generalization of the zero-curvature method, renders the model integrable. We construct explicit non-local non-trivial conserved charges for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber method.

18 pages, 1 figure; v2: references added

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• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• On the unitarity problem in space/time noncommutative theories
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Noncommutative Multi-Solitons in 2+1 Dimensions
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Cited by in corpus (24)

• Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation
• Integrable Noncommutative Sine-Gordon Model
• Noncommutative Solitons and D-branes
• Extension of Noncommutative Soliton Hierarchies
• Isospectral Hamiltonians from Moyal products
• Some properties of the integrable noncommutative sine-Gordon system
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• The U(N) chiral model and exact multi-solitons
• Towards Noncommutative Integrable Equations
• Non-Commutative Geometry from Strings
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Non-commutative solitons and strong-weak duality
• On non commutative sinh-Gordon Equation
• Noncommutative Instantons and Solitons
• Quasideterminant solutions of NC Painlevé II equation with the Toda solution at $n=1$ as a seed solution in its Darboux transformation
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• The quantum sinh-Gordon model in noncommutative (1+1) dimensions
• Abelian Toda field theories on the noncommutative plane
• Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Perturbed nonlinear models from Noncommutativity
• Wave equations associated to Liouville-type problems: global existence in time and blow up criteria
• Noncommmutative solitons and kinks in the affine Toda model coupled to matter
• Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space