# Quantum corrections from a path integral over reparametrizations 

The Niels Bohr International Academy, The Niels Bohr Institute Blegdamsvej 17, 2100 Copenhagen Ø, Denmark ‡ 

Institute of Theoretical and Experimental Physics B. Cheremushkinskaya 25, 117218 Moscow, Russia † 

Yuri Makeenko ∗ 

Poul Olesen ∗ 

(Dated: November 20, 2018) 

## Abstract 

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 

