$Q\bar Q$ potential from AdS-CFT relation at $T\geq 0$: Dependence on orientation in internal space and higher curvature corrections

TL;DR

This paper calculates the static quark-antiquark potential at finite temperature using AdS/CFT, considering higher curvature corrections and internal orientations, revealing critical lines and orientation effects on the potential.

Contribution

It introduces higher curvature corrections and internal orientation dependence into the AdS/CFT calculation of the quark-antiquark potential at finite temperature.

Findings

Critical orientation-distance line shifts with curvature corrections.

No quark-antiquark force beyond the critical line.

String tension for spacelike loops is orientation-independent but background-sensitive.

Abstract

Within the classical approximation we calculate the static $Q\bar Q$ potential via the AdS/CFT relation for nonzero temperature and arbitrary internal orientation of the quarks. We use a higher order curvature corrected target space background. For timelike Wilson loops there arises a critical line in the orientation-distance plane which is shifted to larger distances relative to the calculation with uncorrected background. Beyond that line there is no $Q\bar Q$-force. The overall vanishing of the force for antipodal orientation known from zero tempera ture remains valid. The spacelike Wilson loops yield a string tension for a (2+1)-dimensional gauge theory, independent of the relative internal orientation, but sensitive to the background correction.