Abstract
The static potential is studied in Helfrich and Polyakov's model of smooth strings. For large separations R, the potential is linear in R with corrections of order 1/R. While the physical string tension is renormalized by the extrinsic curvature coupling, the coefficient of the 1/R term has L\"uscher's universal value to any finite order in the loop expansion. For very small separations, the leading term in the potential is proportional to 1/R, with a coefficient exactly twice that of the L\"uscher term, and with corrections that are logarithmically small.
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