Quantum corrections from a path integral over reparametrizations

Understand

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.