Wormholes supported by chiral fields

We consider static, spherically symmetric solutions of general relativity with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields $\mathrm{\Phi }=({\mathrm{\Phi }}^1,\mathrm{.}\mathrm{.}\mathrm{.},{\mathrm{\Phi }}^n)$ (so-called chiral fields) parametrizing a target space with a metric $h_{ab}(\mathrm{\Phi })$. For NSM with zero potential $V(\mathrm{\Phi })$, it is shown that the space-time geometry is the same as with a single scalar field but depends on $h_{ab}$. If the matrix $h_{ab}$ is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.