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Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of (1 + 1)-dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from (2 + 2)-dimensional self-dual U(2) Yang-Mills through a (2 + 1)-dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) --> U(1) to U(2) --> U(1) x U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity. (C) 2004 Elsevier B.V. All rights reserved.

We extend the general method of S.J. Gates Jr. et al. [hep-th/0009192] to compute the consistent gauge anomaly for noncommutative 4d SSYM coupled to chiral matter. The choice of the minimal homotopy path allows us to obtain a simple and compact result. We perform the reduction to components in the WZ gauge proving that our result contains, as lowest component, the busonic chiral anomaly for noncommutative YM theories recently obtained in literature. (C) 2001 Elsevier Science B.V. All rights reserved.

We use the method of Banerjee, Banerjee and Mitra and minimal homotopy paths to compute the consistent gauge anomaly for several superspace models of SSYM coupled to matter, We review the derivation of the anomaly for N = 1 in four dimensions and then discuss the anomaly For two-dimensional models with (2, 0) supersymmetry

In a N = 1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in N = 4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/epsilon (2) pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g(2). We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results. (C) 2001 Elsevier Science B.V. All rights reserved

We discuss features of the 4D, N = 1 WZNW term expressed as a function of chiral superfields and defined in a manner appropriate to calculate phenomenological matrix elements. (C) 2001 Published by Elsevier Science B.V.

We study an integrable quantum field theory of a single stable particle with an infinite number or resonance states. The exact S-matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles inherently. In the limit l --> 0, with l the modulus of the Jacobian elliptic function, it reduces to the Sinh-Gordon S-matrix. We address the problem of computing the form factors of the model by studying their monodromy and recursive equations. These equations turn out to possess infinitely many solutions for any given number of external particles. This infinite spectrum of solutions may be related to the irrational nature of the underlying conformal field theory reached in the ultraviolet limit. We also discuss an elliptic version of the thermal massive Ising model which is obtained by a particular value of the coupling constant. (C) 2000 Elsevier Science B.V. All rights reserved.

By use of a special homotopy operator, we present an explicit, closed-form and simple expression for the left-right Bardeen-Gross-Jackiw anomalies described as the proper superspace integral of a superfunction. (C) 2000 Elsevier Science B.V. All rights reserved