Stochastic loop equations

TL;DR

This paper applies stochastic quantization to derive and analyze loop equations for Wilson loops in large-N gauge theories, connecting them with random contours and supersymmetric quantum mechanics, and exploring both coordinate and momentum representations.

Contribution

It introduces a stochastic quantization approach to Wilson loop equations, establishing links with random contours and supersymmetric quantum mechanics, and derives new equations for the Quenched Master Field and bilocal correlators.

Findings

Derived loop equations in coordinate and momentum representations.

Connected loop equations with supersymmetric quantum mechanics.

Presented a regularized equation for bilocal field correlators.

Abstract

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and the equation for the Quenched Master Field Wilson loop is derived. The regularized version of one of the obtained equations is presented and applied to derivation of the equation for the bilocal field correlator. The momentum loop dynamics is also investigated.