An Introduction to Finite Temperature Quantum Chromodynamics on the Lattice

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In this lecture, we introduce finite temperature QCD on the lattice to non-experts of the subject. We first formulate lattice QCD both at zero and finite temperatures. Then a section is devoted to the topic of improved lattice actions which are becoming an essential ingredient of precision studies of QCD on the lattice. We then discuss about finite temperature SU(3) gauge theory, i.e. QCD without dynamical quarks (quenched QCD). Finally, we report recent status of studies in full QCD taking into account the effects of dynamical quarks. Because of the asymptotic freedom in the UV region, quantum chromodynamics (QCD) is strongly coupled in the IR region. Therefore, it is difficult to study the vacuum structure of QCD by perturbation theory. Two characteristic properties of the QCD vacuum are quark confinement and the spontaneous breakdown of the chiral symmetry. On the other hand, IR properties are affected by temperature. Actually, studies on the lattice have shown that, when the temperature becomes sufficiently high, the low temperature hadronic phase of QCD turns into the high temperature quark-gluon-plasma phase, in which quarks are liberated and chiral symmetry is restored. The quark-gluon-plasma phase is expected to be realized in the early Universe and also possibly in heavy-ion collision experiments. A non-perturbative study is required to understand the QCD vacuum at finite temperatures.