Twisted local systems solve the (holographic) loop equation of large-N QCD_4

TL;DR

This paper develops a holographic approach to solve the loop equation of large-N QCD in 2 and 4 dimensions, using a conformal map and regularized residues to connect to an effective action, providing insights into the theory's structure.

Contribution

It introduces a novel holographic map that simplifies the loop equation of large-N QCD, incorporating a conformal transformation to analyze the effective action.

Findings

Verification with the beta function coefficient supports the approach.

The regularized residue vanishes at the cusp, simplifying calculations.

The method applies to planar self-avoiding loops in large-N QCD.

Abstract

We construct a holographic map from the loop equation of large-N QCD in d=2 and d=4, for planar self-avoiding loops, to the critical equation of an equivalent effective action. The holographic map is based on two ingredients: an already proposed holographic form of the loop equation, such that the quantum contribution is reduced to a regularized residue; a new conformal map from the region encircled by the based loop to a cuspidal fundamental domain in the upper half-plane, such that the regularized residue vanishes at the cusp. As a check, we study the first coefficient of the beta function and that part of the second coefficient which arises from the rescaling anomaly, in passing from the Wilsonian to the canonically normalised (holographic) effective action.