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Anomaly induced transport coefficients, from weak to strong coupling

The existence of new transport phenomena associated to the presence of quantum anomalies has atracted very recently the attention of theorist. These transport coefficient have very interesting properties, for example, they do not renormalize. The most famous case of anomaly induced transport phenomena is the Chiral Magnetic Effect, in which an electric current is produced by a magnetic field if the system has a different number of right handed fermions respect the left handed one. In this thesis we have studied those transport coefficients from Kubo formulas at weak and strong coupling. To finish a fluid/gravity approach is used to compute all the second order anomalous coefficients in an anomalous conformal fluid.