  We demonstrate that, due to the finite thickness of domain walls, and the
consequent ambiguity in defining their locations, the effective string
description obtained by integrating out bulk degrees of freedom contains
ambiguities in the coefficients of the various geometric terms. The only term
with unambiguous coefficient is the zeroth order Nambu-Goto term. We argue that
fermionic ghost fields which implement gauge-fixing act to balance these
ambiguities. The renormalized string tension, obtained after integrating out
both bulk and world-sheet degrees of freedom, can be defined in a scheme
independent manner; and we compute the explicit finite expressions, to
one-loop, for the case of compact quantum electrodynamics and phi-4 theory.
