Wilson loops from supergravity and string theory

We present a theorem that determines the value of the Wilson loop associated with a Nambu-Goto action which generalizes the action of the AdS₅ × S₅ model. In particular, we derive sufficient conditions for confining behaviour. We then apply this theorem to various string models. We go beyond the classical string picture by incorporating quadratic quantum fluctuations. We show that the bosonic determinant of D_p-branes with 16 supersymmetries yields a Lüscher term. We confirm that the free energy associated with a BPS configuration of a single quark is free from divergences. We show that unlike for a string in flat spacetime in the case of AdS₅ × S₅ the fermionic determinant does not cancel the bosonic one. For a set-up that corresponds to a confining gauge theory the correction to the potential is attractive. We determine the form of the Wilson loop for actions that include non-trivial B_μν field. The issue of an exact determination of the value of the stringy Wilson loop is discussed.