Hadronic spectral functions in QCD

Among many other observables in QCD, the spectral function (SPF) is the simplest but most interesting dynamical quantity. It can be studied both from the QCD action (QCD sum rules, lattice QCD etc) and from the effective hadronic action. Also, SPFs are either directly or closely related to the experimental data. Namely, SPFs are the observables through which we can directly compare theory and experiment without much intermediate interface. In relation to the physics of chiral symmetry and its restoration in hot/dense matter, SPFs of light vector mesons (ρ, ω and φ) are most relevant since they can be observed by dileptons. SPF of scalar-isoscalar ''σ'' could be also interesting: ''σ'' dose not show up clearly in the vacuum because of it huge width decaying into two pions, but it may appear as a soft and narrow collective mode when the chiral symmetry is (partially) restored. In relation to the deconfinement of quarks in hot/dense matter, SPFs of heavy mesons such as J/Ψ and Ψ' are most relevant. (author)