The structure of the phase diagram for strong interactions becomes richer in the presence of a magnetic background, which enters as a new control parameter for the thermodynamics. Motivated by the relevance of this physical setting for current and future high-energy heavy-ion collision experiments and for the cosmological QCD transitions, we use the linear sigma model coupled to quarks and to Polyakov loops as an effective theory to investigate how the chiral and the deconfining transitions are affected, and present a general picture for the temperature\char21{}magnetic field phase diagram. We compute and discuss each contribution to the effective potential for the approximate order parameters, and uncover new phenomena such as the paramagnetically induced breaking of global Z3 symmetry, and possible splitting of deconfinement and chiral transitions in a strong magnetic field.

The presence of a strong magnetic background can modify the nature and the dynamics of the chiral phase transition at finite temperature. We compute the modified effective potential in the linear sigma model with quarks to one loop in the $\overline{\mathrm{MS}}$ scheme for $N_f=2$. For fields $eB\sim 5m_{\pi }^2$ and larger a crossover is turned into a weak first-order transition. We discuss possible implications for noncentral heavy ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider and for the primordial QCD transition.

We compute the one-loop thermomagnetic corrections to the self-coupling in a model where charged scalars interact also with a constant magnetic field. The calculation is motivated by the possibility that the critical temperature for the chiral phase transition in a magnetic background can be influenced by the dependence of the coupling constant on the magnetic field. We show that the coupling decreases as a function of the field strength. This functional dependence introduces in turn a correction to the boson masses which causes the critical temperature to decrease as a function of the field strength.

An effective quantum field theory description of graphene in the ultrarelativistic regime is given by reduced quantum electrodynamics (QED) also known as pseudo QED also known as mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting conformal field theories (CFT) in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the $\beta$-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a nonsupersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.