Wilson loops from supergravity and string theory

Abstract

We present a theorem that determines the value of the Wilson loop associated with a Nambu-Goto action which generalizes the action of the $AdS_5\times S_5$ model. In particular we derive sufficient conditions for confining behavior. 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 Luscher 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 space time in the case of $AdS_5\times S_5$ the fermionic determinant does not cancel the bosonic one. For a setup 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. Talk presented in string 99 Potsdam.