Exact classical solutions of nonlinear sigma models on supermanifolds

Ryu Sasaki; Wen-Li Yang; Yao-Zhong Zhang

doi:10.1016/j.nuclphysb.2007.03.013

paper

Exact classical solutions of nonlinear sigma models on supermanifolds

arXiv:hep-th/0612154 · doi:10.1016/j.nuclphysb.2007.03.013

Abstract

We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds $G (m, p ∣ n, q) ≅ U (m ∣ n) / [U (p ∣ q) \otimes U (m - p ∣ n - q)]$ for $0 \leq p \leq m$ , $0 \leq q \leq n$ and $1 \leq p + q$ . The projective superspace $CP^{m - 1∣ n}$ is a special case of $p = 1$ , $q = 0$ . For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm-Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super case published more than twenty years ago by one of the present authors.

Latex file, 17 pages; V2, typos corrected, this version will appear in Nucl. Phys. B