Center-stabilized Yang-Mills theory: Confinement and large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>volume independence

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 ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ with a sufficiently small compactification size $L$, then an analytic treatment of the nonperturbative 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.