ITEP–TH–03/10 Quantum corrections from a path integral over reparametrizations Yuri Makeenko ∗ Poul Olesen ∗ (Dated: November 20, 2018) Institute of Theoretical and Experimental Physics B. Cheremushkinskaya 25, 117218 Moscow, Russia † The Niels Bohr International Academy, The Niels Bohr Institute Blegdamsvej 17, 2100 Copenhagen Ø, Denmark ‡ We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large- N QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the L¨ uscher term associated with d = 26 dimensions and propose a modification of the ansatz which reproduces the L¨ uscher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the L¨ uscher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly. PACS numbers: 11.15.Pg, 11.25.Tq, 12.38.Aw $^{∗}$Also at the Institute for Advanced Cycling, Blegdamsvej 19, 2100 Copenhagen Ø, Denmark $^{†}$Electronic address: makeenko@itep.ru $^{‡}$Electronic address: polesen@nbi.dk 1 Abstract arXiv:1002.0055v1 [hep-th] 31 Jan 2010