On the extraction of spectral densities from lattice correlators: a study of the QCD electromagnetic conductivity in the presence of an external magnetic field.

This work pursues a double aim. The first one is to provide a better understanding of the properties of the QCD phase diagram in the presence of an external magnetic field, a topic whose understanding has been recently updated, but which needs a better characterization from a phenomenological point of view: we will try to provide such characterization by studying transport coefficients, in particular the electromagnetic conductivity of the strongly interacting medium. The second purpose, arising within this context, is to investigate and compare different methods which are presently used to extract transport coefficients from Euclidean time correlators measured in lattice QCD simulations: this is an issue pertaining to the most general problem of the inverse Laplace transform, which arises in several and quite different fields of Physics