Extended supersymmetric σ-model based on the image Lie algebra of the fermion operators Original Research Article

Extended supersymmetric σ-model is given, standing on the image Lie algebra of fermion operators composed of annihilation–creation operators and pair operators. Canonical transformation, the extension of the image Bogoliubov transformation to the image group, is introduced. Embedding the image group into an image group and using image coset variables, we investigate a new aspect of the supersymmetric σ-model on the Kähler manifold of the symmetric space image. We construct a Killing potential which is just the extension of the Killing potential in the image coset space given by van Holten et al. to that in the image coset space. To our great surprise, the Killing potential is equivalent with the generalized density matrix. Its diagonal-block matrix is related to a reduced scalar potential with a Fayet–Ilipoulos term. The reduced scalar potential is optimized in order to see the behaviour of the vacuum expectation value of the σ-model fields and a proper solution for one of the image group parameters is obtained. We give bosonization of the image Lie operators and vacuum functions in terms of the image coset variables, a image phase and the corresponding Kähler potential.