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 models, which includes the near horizon limit of D-P branes with 16 supersymmetries, 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 the bosonic and the fermionic determinants cancel, in particular confirming the absence of divergences. We find that for the Wilson loop in that model, however, there is no such cancellation. For string models that correspond to 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 Science B.V. All rights reserved.