Static potential for smooth strings in the large-Dlimit

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Abstract
The static potential V(R) in Polyakov’s model of smooth strings is studied in the large-D limit. The physical string tension is calculated analytically as a function of the bare string tension and the extrinsic curvature coupling. A systematic saddle-point method for computing the loop expansion of V(R) is developed and carried out explicitly to two loops. There are no corrections to the 1/R Luscher term to this order. The leading short-distance behavior of V(R) is also proportional to 1/R with twice the coefficient of the Luscher term.