We discuss the impact of quadratic quantum fluctuations on the Wilson loop
extracted from classical string theory. We show that a large class of model
s, which includes the near horizon limit of D-P branes with 16 supersymmetr
ies, admits a Luscher type correction to the classical potential. For a BPS
configuration of a single quark in the AdS(5) x S-5 model, we show that th
e bosonic and the fermionic determinants cancel, in particular confirming t
he absence of divergences. We find that for the Wilson loop in that model,
however, there is no such cancellation. For string models that correspond t
o gauge theories in the confining phase, we show that the correction to the
potential is of a Luscher type and is attractive. (C) 2000 Elsevier Scienc
e B.V. All rights reserved.