Effective QCD string beyond Nambu-Goto

We consider the QCD string as an effective string, whose action describes long-range stringy fluctuations. The leading infrared contribution to the ground state energy is given by the Alvarez-Arvis formula, usually derived using the Nambu-Goto action. Here we rederive it by a saddle point calculation using the Polyakov formulation of the free string, where the world sheet metric and the target space coordinates are treated as independent variables. The next order relevant in the infrared term in the effective action is the extrinsic curvature term. We show that the spectrum does not change order by order in the inverse string length, but may change at intermediate distances.