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-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 M S scheme for N f = 2. For fields eB ∼ 5m 2 π and larger a crossover is turned into a weak first-order transition. We discuss possible implications for non-central heavy ion collisions at RHIC and LHC, 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.

We study the nature of the chiral transition for an effective theory with spontaneous breaking of symmetry, where charged bosons and fermions are subject to the effects of a constant external magnetic field. The problem is studied in terms of the relative intensity of the magnetic field with respect to the mass and the temperature. When the former is the smallest of the scales, we present a suitable method to obtain magnetic and thermal corrections up to ring order at high temperature. By these means, we solve the problem of the instability in the boson sector for these theories, where the squared masses, taken as functions of the order parameter, can vanish and even become negative. The solution is found by considering the screening properties of the plasma, encoded in the resummation of the ring diagrams at high temperature. We also study the case where the magnetic field is the intermediate of the three scales and explore the nature of the chiral transition as we vary the field strength, the coupling constants and the number of fermions. We show that the critical temperature for the restoration of chiral symmetry monotonically increases from small to intermediate values of the magnetic fields and that this temperature is always above the critical temperature for the case when the magnetic field is absent.Comment: 13 pages, 6 figures, added comments. Version to appear in Phys. Rev

An effective quantum field theory description of graphene in the ultra-relativistic regime is given by reduced QED aka. pseudo QED aka. 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 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 β-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 non-supersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.

We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU 2 gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the Markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise.

We study the effects of CP violation on the nature of the chiral transition within the linear sigma model with two flavors of quarks. The finite-temperature effective potential containing contributions from nontrivial values for the parameter θ is computed to one loop order and their minima structure is analyzed. Motivated by the possibility of observing the formation of CP-odd domains in highenergy heavy ion collisions, we also investigate the behavior of the effective potential in the presence of a strong magnetic background. We find that the nature of the chiral transition is influenced by both θ and the magnetic field.

We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this non-local but still gauge invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz non-invariant case due to the Fermi velocity v F < c. This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of (2 + 1)-dimensional planar reduced QED.Keywords: Reduced QED, dynamical Chern-Simons term. * david.dudal@kuleuven.be † ana.mizher@kuleuven.be ‡ pablo.pais@kuleuven.be I. CONTEXT AND MOTIVATIONQuantum Electrodynamics in (2 + 1) dimensions (QED 3 ) has been widely used as a toy model for Quantum Chromodynamics (QCD). This is due to the fact that although being Abelian, QED 3 exhibits similar features as non-Abelian gauge theories, making it possible, for instance, to map and investigate chiral symmetry breaking and confinement into it [1][2][3][4][5]. The similarity is reinforced by the fact that a non-Abelian gauge theory at high temperature suffers a dimensional reduction and, if coupled to N f fermion families, the non-Abelian interactions are suppressed by a factor of N −1 f , so that in the large N f limit the theory can be considered approximately Abelian.Recently, the emergence of the so-called Dirac and Weyl planar materials [6], converted QED 3 into a playground in which a potential link between high energy physics (including quantum fields in curved spacetimes) and condensed matter can emerge [7][8][9][10][11][12][13]. Those are materials in which, due to the specific structure of their underlying lattice, the charge carriers present a relativistic-like behavior, being correctly described by a Dirac-like equation in some regimes. Particularly, the physical realization of graphene and other materials in two space dimensions, that are proved to contain a priori massless Dirac spinors, naturally yields the fermionic part of QED 3 [14, 15] through the continuum limit of the tight-binding theory, usually applied to describe their conduction electrons, which in turn implies a direct connection to QCD, as discussed above.Nevertheless, even though in these systems the fermions are constrained to remain in-plane and therefore are correctly described by a theory in (2 + 1) dimensions, the gauge fields responsible for the interaction between these electrons are not subject to the same constraint. One of the most remarkable consequences of this fact is that the interaction between electrons remains the familiar ∼ 1/r potential rather than the logarithmic one that would take place if the gauge fields were also restricted to the plane. Therefore, it is convenient and necessary to modify QED 3 in order to merge the desired features of the two sectors of the theory, starting with a general (3 + 1) theory and dimensionally reducing it to a non-local effective (2 ...