  We study elastic manifolds with self-repelling terms and estimate their
effective radius. This class of manifolds is modelled by a self-repelling
vector-valued Gaussian free field with Neumann boundary conditions over the
domain $[-N,N]^d\cap \mathbb{Z}^d$, that takes values in $\mathbb{R}^d$. Our
main result states that in two dimensions ($d=2$), the effective radius $R_N$
of the manifold is approximately $N$. This verifies the conjecture of Kantor,
Kardar and Nelson [8] up to a logarithmic correction. Our results in $d\geq 3$
give a similar lower bound on $R_N$ and an upper of order $N^{d/2}$. This
result implies that self-repelling elastic manifolds undergo a substantial
stretching at any dimension.
