Comments on Noncommutative Sigma Models

Abstract

We review the derivation of a noncommutative version of the nonlinear sigma model on $\CPn$ and it's soliton solutions for finite $\theta$ emphasizing the similarities it bears to the GMS scalar field theory. It is also shown that unlike the scalar theory, some care needs to be taken in defining the topological charge of BPS solitons of the theory due to nonvanishing surface terms in the energy functional. Finally it is shown that, like its commutative analogue, the noncommutative $\CPn$-model also exhibits a non-BPS sector. Unlike the commutative case however, there are some surprises in the noncommutative case that merit further study.

22 pages, 4 figures, LaTeX (JHEP3), Minor changes, Discussion expanded and references added

References in corpus (3)

• Vacuum String Field Theory ancestors of the GMS solitons
• Non-BPS Solutions of the Noncommutative CP^1 Model in 2+1 Dimensions
• General classical solutions in the noncommutative CP^(N-1) model

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• Integrable Noncommutative Sine-Gordon Model
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model
• Lost equivalence of nonlinear sigma and $C{P}^1$ models on noncommutative space
• Transmogrifying Fuzzy Vortices
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space