A finite box as a tool to distinguish free quarks from confinement at high temperatures

Above the pseudocritical temperature $$T_c$$ T c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined.

Aspects on Effective Theories and the QCD Transition

We review recent advances in the understanding of the Quantum Chromodynamics (QCD) transition and its nature, paying special attention to the analysis of chiral symmetry restoration within different approaches based on effective theories. After presenting some of the main aspects of the current knowledge of the phase diagram from the theoretical, experimental and lattice sides, we discuss some recent problems where approaches relying on effective theories have been particularly useful. In particular, the combination of ideas such as Chiral Perturbation Theory, unitarity and Ward Identities allows us to describe successfully several observables of interest. This is particularly relevant for quantities expected to be dominated by the light meson components of the hadron gas such as the scalar and topological susceptibilities. In addition, ward identities and effective Lagrangians provide systematic results regarding chiral and U ( 1 ) A partner degeneration properties which are of great importance for the interplay between those two transitions and the nature of chiral symmetry restoration. Special attention is paid to the connection of this theoretical framework with lattice simulations.