Quantum fluctuations of Wilson loops from string models

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.