Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence

TL;DR

This paper introduces a double trace deformation of SU(N) Yang-Mills theory that maintains volume independence at large N and small volumes, enabling analytic control over confinement and mass gap in a controlled setting.

Contribution

It demonstrates that the deformed Yang-Mills theory preserves large N volume independence and allows analytic study of confinement and mass gap at small volumes and N, unlike unmodified theory.

Findings

Large N volume independence holds in the deformed theory.

The deformed theory exhibits a mass gap and linear confinement at small compactification size.

The approach generalizes to QCD-like theories.

Abstract

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.