Large-N limit and contact terms in unbroken YM_4

TL;DR

This paper analyzes the structure of the master field in large-N 4D Yang-Mills theory on a product of Riemann surfaces, revealing contact terms and their relation to confinement and flat connections.

Contribution

It characterizes the master field structure in large-N YM_4, highlighting contact terms and their compatibility with large-N factorization and confinement.

Findings

Master field includes bulk and contact terms.

Contact terms arise from localization at N=∞.

In confining theories, measure localizes on flat connections with punctures.

Abstract

I characterize the structure of the master field for $F^{0}_{z \bar z}$ in $SU(\infty)$-$YM_4$ on a product of two Riemann surfaces $Z \times W$ in the gauge $F^{ch}_{z \bar z}=0$ as the sum of a `bulk' constant term and of delta-like `contact' terms.\\ The contact terms may occur because the localization of the functional integral at $N=\infty$ on a master orbit of a constant connection under the action of singular gauge transformations is still compatible with the large-$N$ factorization and translational invariance.\\ In addition I argue that if the gauge group is unbroken and there is a mass gap, that is if the theory confines, the functional measure at $N=\infty$, in the gauge $F^{ch}_{z \bar z}=0$, must be localized on the moduli space of flat connections with punctures on $Z \times W$.