We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual

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... y backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative L'(r_0)>0. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.