| Summary: | We use a deformed “center-stablised” gauge theory, which can be brought into a weak coupling regime while remaining confined and gapped, as a toy model to study some ideas from real QCD. The deformed model has the correct nontrivial θ-dependence and degeneracy of topological sectors conjectured for QCD, and is, apparently, smoothly connected to the strongly coupled undeformed Yang-Mills, so that we can perhaps expect to get some qualitative insights into QCD. We demonstrate the presence of a nondispersive contact term in the topological susceptibility, which contributes with the opposite sign to normal dispersive contributions coming from physical propagating degrees of freedom. We further show that, despite the system being completely gapped with no massless physical degrees of freedom, the system has a Casimir-like, power scaling, dependence on boundaries, in contrast with the naive expectation that a system with only massive degrees of freedom should have a weak (exponentially small) dependence on long distance effects. This behaviour suggests the possibility for a solution for the cosmological dark energy problem coming from the strongly coupled QCD sector on a manifold with a boundary, which would have the correct sign and be of the correct order of magnitude. Next, we investigate the interaction between point-like topological charges (monopoles) and extended sheet-like topological defects (domain walls) in attempt to explain some recent lattice QCD results suggesting that extended topological objects are more important to understanding the relevant field configurations in QCD than the instantons traditionally expected. Finally, we derive the existence of excited metastable vacuum states and calculate their decay rate to the true ground state of the theory, comparing with the expected results discussed years ago in proper QCD. The presence of metastable vacuum states with a nonzero effective θ parameter, like those present in the deformed model, could explain P and CP violation in heavy ion collisions observed on an event by event basis, which seem to average away over many events. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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