  A lower bound on the size of a Lorentzian wormhole can be obtained by
semiclassically introducing the Planck cut-off on the magnitude of tidal forces
(Horowitz-Ross constraint). Also, an upper bound is provided by the quantum
field theoretic constraint in the form of the Ford-Roman Quantum Inequality for
massless minimally coupled scalar fields. To date, however, exact static
solutions belonging to this scalar field theory have not been worked out to
verify these bounds. To fill this gap, we examine the wormhole features of two
examples from the Einstein frame description of the vacuum low energy string
theory in four dimensions which is the same as the minimally coupled scalar
field theory. Analyses in this paper support the conclusion of Ford and Roman
that wormholes in this theory can have sizes that are indeed only a few order
of magnitudes larger than the Planck scale. It is shown that the two types of
bounds are also compatible. In the process, we point out a "wormhole" analog of
naked black holes.
