Exact classical solutions of nonlinear sigma models on supermanifolds

Abstract

We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds $G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for $0\le p\le m$, $0\le q\le n$ and $1\le p+q$. The projective superspace ${\mathbf{CP}}^{m-1|n}$ 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.

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

References in corpus (7)

• Riemannian symmetric superspaces and their origin in random matrix theory
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Conformal Sigma-Models on Supercoset Targets
• Conserved Charges in the Principal Chiral Model on a Supergroup