Study of phase transitions in quantum chromodynamics using the holographic duality method

One of the most important problem in the quantum theory of strong interactions of elementary particles - quantum chromodynamics - is the description of confinement/deconfinement phase transition. In the Aref'eva papers [1,2,3] important results in solving this problem using the holographic duality are obtained. For this purpose, black holes/black branes solutions in 5-dimensional dilaton gravity interacting with Maxwell fields, that describe the holographic renormalization group flow reproducing the chromodynamics renormalization group flow are constructed. This renormalization group flow interpolates between the ultraviolet region with asymptotic freedom and quark confinement in the infrared region. A characteristic property of the constructed solutions is a spatial anisotropy. Consideration of collisions of shock waves on the constructed anisotropic background gives the dependence of the entropy on energy, consistent with the dependence on the energy of the multiplicity of particles produces in collisions of heavy ions. The anisotropic background predicts a smeared nature of the confinement/deconfinement phase transition. The dependence on the anisotropy parameter of the thermalization time and diffusion coefficients associated with the photon production in heavy ion collisions is established.