285503 Lattice QCD at finite temperature and density (V) (SoSe 2012)

A course on the phases and phase transitions of strong interactions analyzed with the methods of
lattice �eld theory. Discussions and comparisons with other theoretical approaches will be included
as well.
1 - Introduction and background material [3 units]
A historical introduction to the discovery of new phases of QCD motivates the introduction of lattice
�eld theory methods for their analysis.
2 - The high temperature transition [4 units]
After introducing con�nement and chiral symmetry the high temperature transition is discussed both
for pure gauge and fermionic systems. Symmetry aspects are highlighted, and the universal language
of the magnetic equation of state is introduced and applied to several cases of interest. The lattice
technical aspects introduced here include �nite size scaling and the approach to the continuum limit
using di�erent lattice discretizations.
3 - QCD at �nite density [4 units]
The phenomenological analysis of the phase diagram based on model �eld theories and random matrix
models are discussed �rst, making contact with basic aspects of the thermodynamics of a dense system.
The lattice formulation of �nite baryon density is introduced, alongside with the sign problem. The
strong coupling expansion is reviewed, before turning to relevant models which do not su�er from the
sign problem, such as QCD at �nite isospin density. The current understanding of the phase diagram
in the temperature, baryon chemical potential, isospin chemical potential is presented in detail.
4 - Practical tools for QCD with a small baryon density [4 units]
Various methods for analysing QCD at small baryon density and high temperature are reviewed and
compared, including the possibility of hybrid methods. Canonical and grandcanonical ensemble and
their interrelation, as well as general tools for the analysis of the phase diagram in a generalized space
with complex couplings - Lee Yang zeros { are included in this section.
5 - Quark Gluon Plasma [3 units]
Devoted to the properties of the hot medium above the critical temperature, from the strongly in-
teractive quark gluon plasma to the ideal free gas. The interactions in the plasma and its transport
properties are discussed introducing spectral functions and relevant thermodynamic observables. The
melting pattern of quarkonia emerging from various lattice approaches is outlined, alongside their
possible experimental signatures. The status of various theoretical conjectures on the nature of the
strongly interactive quark gluon plasma, and the role of lattice in discriminating among them is re-
viewed.
6 - Complements - to be discussed with the participants [2 units]
The course is supplemented by a privatissime seminar.
ekVV 285503, module 55, 6LP when exam is included, course language is English, starts April 23rd