Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.Comment: 10 pages, 1 figure, added references for sections 1 and

Magnetic Catalysis: A Review

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.Comment: 37 pages, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee. Version 2: references adde

Lattice QCD Simulations in External Background Fields

We discuss recent results and future prospects regarding the investigation, by lattice simulations, of the non-perturbative properties of QCD and of its phase diagram in presence of magnetic or chromomagnetic background fields. After a brief introduction to the formulation of lattice QCD in presence of external fields, we focus on studies regarding the effects of external fields on chiral symmetry breaking, on its restoration at finite temperature and on deconfinement. We conclude with a few comments regarding the effects of electromagnetic background fields on gluodynamics.Comment: 31 pages, 10 figures, minor changes and references added. To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye