Abstract
We examine a double trace deformation of Yang-Mills theory which, for large and large volume, is equivalent to unmodified Yang-Mills theory up to corrections. In contrast to the unmodified theory, large 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 volume independence in small volumes. For small values of , if the theory is formulated on with a sufficiently small compactification size , 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 or number of colors 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 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 it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.
- Received 21 March 2008
DOI:https://doi.org/10.1103/PhysRevD.78.065035
©2008 American Physical Society