  With the use of the world-line formalism, the heavy-quark condensate in the
SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the
quark-antiquark potential at short distances is either quadratic, or linear. In
the former case, which takes place in the stochastic vacuum model, the standard
QCD-sum-rules result is reproduced. In the other case, the condensate turns out
to be UV-finite only in less than four dimensions. This fact excludes a
possibility to have, in four dimensions, the linear term in the potential, as
well as short strings, at the distances smaller than the vacuum correlation
length. The use of the world-line formalism enables one to generalize further
both results for the condensate to the case of finite temperatures. A
generalization of the QCD-sum-rules result to the case of an arbitrary number
of space-time dimensions is also obtained and turns out to be UV-finite,
provided this number is smaller than six.
