Thermal Electromagnetic Radiation in Heavy-Ion Collisions

We review the potential of precise measurements of electromagnetic probes in relativistic heavy-ion collisions for the theoretical understanding of strongly interacting matter. The penetrating nature of photons and dileptons implies that they can carry undistorted information about the hot and dense regions of the fireballs formed in these reactions and thus provide a unique opportunity to measure the electromagnetic spectral function of QCD matter as a function of both invariant mass and momentum. In particular we report on recent progress on how the medium modifications of the (dominant) isovector part of the vector current correlator ($\rho$ channel) can shed light on the mechanism of chiral symmetry restoration in the hot and/or dense environment. In addition, thermal dilepton radiation enables novel access to (a) the fireball lifetime through the dilepton yield in the low invariant-mass window $0.3 \; \mathrm{GeV} \leq M \leq 0.7 \; \mathrm{GeV}$, and (b) the early temperatures of the fireball through the slope of the invariant-mass spectrum in the intermediate-mass region ($1.5 \; \mathrm{GeV} <M< 2.5 \; \mathrm{GeV}$). The investigation of the pertinent excitation function suggests that the beam energies provided by the NICA and FAIR projects are in a promising range for a potential discovery of the onset of a first order phase transition, as signaled by a non-monotonous behavior of both low-mass yields and temperature slopes.