Finite Size Effects and Conformal Symmetry of O(N)O(N) Nonlinear σ\sigma Model in Three Dimensions

We study the $O(N)$ nonlinear $\sigma$ model on a three-dimensional compact space $S^1 \times S^2$ (of radii $L$ and $R$ respectively) by means of large $N$ expansion, focusing on the finite size effects and conformal symmetries of this model at the critical point. We evaluate the correlation length and the Casimir energy of this model and study their dependence on $L$ and $R$. We examine the modular transformation properties of the partition function, and study the dependence of the specific heat on the mass gap in view of possible extension of the $C-$theorem to three dimensions.Comment: 12 pages uuencoded compressed PostScript file including 1 figur

Ultraviolet Property of Noncommutative Wess-Zumino-Witten Model

We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The \beta-function of the U(N) noncommutative WZW model resembles that of the ordinary WZW model. The U(1) noncommutative model has also a nontrivial fixed point.Comment: 7 pages, 1 figur

Instanton Equations for the Supersymmetric CP^{N-1} Sigma Model on Non(anti)commutative Superspace

We study the instanton equation of the supersymmetric CP^{N-1} sigma model on non(anti)commutative superspace in two dimensions. We show that the undeformed instanton equation is consistent with the deformed equations of motion. Then we conclude that the instanton equation is not deformed by superspace non(anti)commutativity.Comment: 6 page

Vanishing Next-to-Leading Corrections to the \beta-Function of the SUSY CP^{N-1} Model in Three Dimensions

We study the ultraviolet properties of the supersymmetric CP^{N-1} sigma model in three dimensions to next-to-leading order in the 1/N expansion. We calculate the \beta-function to this order and verify that it has no next-to-leading order corrections.Comment: 8 pages, 1 figure, the renormalization constant of the field alpha is correcte