Quantum fluctuations of Wilson loops from string models

Abstract

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 Lüscher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS 5 ×S 5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a Lüscher type and is attractive.

Wilson loops in SYM theory: From weak to strong coupling

“…Our main emphasis will be on the exact results and we will omit several interesting issues which are discussed extensively elsewhere. Notable omissions are computation of quantum corrections to Wilson loops due string fluctuations [23,24,25,26,27,8], the instanton contribution to Wilson loop expectation values [28,29], and extensions to less supersymmetric and non-conformal examples of gauge theory / gravity correspondence. Wilson loops in the that context are reviewed in [30].…”

On the holographic duals of N = 1 gauge dynamics.

“…Such stringy corrections will change the string tension, but keep the leading linear L dependence. Another source of stringy corrections that becomes relevant in Wilson loop calculations is the fluctuating worldsheet [24,25,26,27]. Since the classical configuration is a flat horizontal string, these corrections will lead to a quark anti-quark potential with a Lüscher term correction of the form…”

“…The S 3 stays at a finite radius proportional to √ g s N . The number of massless bosonic excitations will thus be n b = 8 (or 7 according to [24]) if the distance between the quarks is smaller than the radius of S 3 , and n b = 5 if it is larger.…”

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

“…Moreover, the area-law prescription Eq. (6.5) carries over to the confining case, substituting the AdS metric with an appropriate confining background [38,39,40] and replacing 1/(2πα ′ ) with an effective string tension 1/(2πα ′ eff ). At this point, one has to substitute the area-law expression Eq.…”