It is known since 1980s that both conformal field theory technique and
lattice regularizations of a quantum string work only in the target-space dimension
d<2. As we have shown recently with Jan Ambjorn, the usual classical string
vacuum is unstable for d>2, where another quantum vacuum state has lower
energy and is stable under fluctuations for d<26. I construct it in the mean-field
approximation which is analogous to solving the sigma-model at large N and
show how the results known from canonical quantization are reproduced.
This requires a very special scaling limit whose existence is due to the fact that
the worldsheet metric becomes singular when the cutoff is removed.
