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

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.

Used background has been adapted to hep-th/9808126 and revised version of hep-th/9805156, slightly changed comment on 1/L term