No abstract

We study a number of different ingredients related to the θ dependence, metastable excited vacuum states and other related subjects using a simplified version of QCD, the so-called "deformed QCD". This model is a weakly coupled gauge theory, which, however, preserves all the relevant essential elements allowing us to study hard and nontrivial features which are known to be present in real strongly coupled QCD. Our main focus in this work is to test the ideas related to the metastable vacuum states (which are known to be present in strongly coupled QCD in large N limit) in a theoretically controllable manner using the "deformed QCD" as a toy model. We explicitly show how the metastable states emerge in the system, why their lifetime is large, and why these metastable states must be present in the system for the self-consistency of the entire picture of the QCD vacuum. We also speculate on possible relevance of the metastable vacuum states in explanation of the violation of local P and CP symmetries in heavy ion collisions. Crown

We propose that the solution to the cosmological vacuum energy puzzle may come from the infrared sector of the effective theory of gravity, where the impact of the trace anomaly is of upmost relevance. We proceed by introducing two auxiliary fields, which are capable of describing a diversity of quantum states via specification of their macroscopic (IR) boundary conditions, in contrast to ultraviolet quantum effects. Our investigation aims at finding a realistic cosmological solution which interprets the observed cosmological constant as a well defined deficit in the zero point energy density of the Universe. The energy density arises from a phase transition, which alters the properties of the quantum ground state. We explicitly formulate low energy gravity as an effective field theory with a precise definition of the "point of normalization" as the point at which the "renormalized cosmological constant" is set to zero in the Minkowski vacuum, in which the Einstein equations are automatically satisfied as the Ricci tensor identically vanishes. With this definition the effective QFT of gravity has a predictive power. In particular, it must predict the evolution of the system in any nontrivial geometry, including the vacuum energy behaviour as a function of infrared, rather than ultraviolet, input parameters.

We study a number of different ingredients related to long range order observed in lattice QCD simulations, using a simple ''deformed QCD'' model. This model is a weakly coupled gauge theory, which, however, has all the relevant crucial elements, allowing us to study difficult and nontrivial problems which are known to be present in real, strongly coupled QCD. In the present study, we want to understand the physics of long range order in the form of coherent low-dimensional vacuum configurations observed in Monte Carlo lattice simulations. We demonstrate the presence of double-layer domain wall structures in the deformed QCD, and study their interaction with localized topological monopoles. Furthermore, we show that there is in fact an attractive interaction between the two, such that the monopole favors a position within the domain wall.

We study a Casimir-like behaviour in a "deformed QCD". We demonstrate that for the system defined on a manifold of size L the difference ∆E ≡ E − E Mink between the energies of a system in a non-trivial background and Minkowski space-time geometry exhibits the Casimir-like scaling ∆E ∼ L −1 , despite the presence of a mass gap in the system, in contrast with naive expectation ∆E ∼ exp(−mL), which would normally originate from any physical massive propagating degrees of freedom consequent to conventional dispersion relations. The Casimir-like behaviour in our system comes instead from a non-dispersive ("contact") term which is not related to any physical propagating degrees of freedom, such that the naive argument is simply not applicable. These ideas can be explicitly tested in weakly coupled deformed QCD. We comment on profound consequences for cosmology of this effect if it persists in real strongly coupled QCD.