Quantum fluctuations of Wilson loops from string models

TL;DR

This paper analyzes how quadratic quantum fluctuations influence Wilson loops in string models, revealing Lüscher-type corrections and differences in fermionic and bosonic determinants, with implications for gauge theories.

Contribution

It demonstrates the presence of Lüscher-type quantum corrections to Wilson loops in various string models, including confining gauge theories, and clarifies determinant behaviors in supersymmetric backgrounds.

Findings

Lüscher-type correction appears in several string models including D_p branes.

Fermionic determinants do not cancel bosonic ones in AdS_5 x S^5.

Quantum corrections are attractive in confining gauge theories.

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 L\"{u}scher 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 \times 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 L\"{u}scher type and is attractive.