  Quantum Chromodynamics (QCD) is the fundamental theory of strong
interactions. It describes the behavior of quarks and gluons which are the
smallest known constituents of nuclear matter. The difficulties in solving the
theory at low energies in the strongly interacting, non-perturbative regime
have left unanswered many important questions in QCD, such as the nature of
confinement or the mechanism of hadronization. In these lectures oriented
towards the students we introduce two classes of dualities that attempt to
reproduce many of the features of QCD, while making the treatment at strong
coupling more tractable: (1) the AdS/CFT correspondence between a specific
class of string theories and a conformal field theory and (2) an effective
low-energy theory of QCD dual to classical QCD on a curved conformal
gravitational background. The hope is that by applying these dualities to the
evaluation of various properties of the strongly-interacting matter produced in
heavy ion collisions one can understand how QCD behaves at strong coupling. We
give an outline of the applications, with emphasis on two transport
coefficients of QCD matter -- shear and bulk viscosities.
