Smooth strings at large dimension

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Abstract
Surfaces embedded in d Euclidean dimensions with an extrinsic curvature term are investigated. To one-loop order, the effective action for metric fluctuations has a Liouville form over both large and short distances. At large distances, the Liouville theory is the same as for the Nambu model, ∼26-d. At short distances, the Liouville action is proportional to 26-2d; this produces negative eigenvalues, and so instability, unless d≤13. At large d, this instability is overlooked to compute correlation functions by an expansion in ∼1/d. There is a critical point when the renormalized string tension vanishes, with the only infrared singular correlations those of the Liouville theory over large distances, ∼26-d. At the critical point, there is also a tachyon at nonzero momentum; tachyons probably do not occur if d