(Inverse) Magnetic Catalysis

QCD breaks chiral symmetry at low energies. An interesting question then arises how this process is affected by the presence of a magnetic field. From perturbation theory one would expect that the chiral symmetry breaking is enhanced, but around the QCD phase transition lattice computations find the opposite, a phenomenon called inverse magnetic catalysis (IMC). In [1], we were able to see IMC in a holographic model. Below, on the left I show the phase diagram, and on the right lines of constant chiral condensate, clearly indicating IMC.

We were also able to corroborate the findings in lattice QCD that (inverse) magnetic catalysis is due to two competing effects, where one gets magnetic catalysis if one effect dominates, and inverse magnetic catalysis if the other effect dominates. In [2], we also added a baryon chemical potential to the holographic model. This allows to study IMC in a regime where lattice QCD cannot perform reliable computations. Below, I show on the left the chiral transition temperature as a function of chemical potential for different values of magnetic field. One can see that for small chemical potentials the chiral transition temperature decreases with the magnetic field B, while the opposite is true at large chemical potentials. On the right, I show near B = 0 for which values of temperature and chemical potential one get magnetic catalysis or the opposite.

In [3], we turned both the magnetic field and chemical potential off, and instead added an anisotropy a in the form of a space-dependent theta term. Below, the quantity on the vertical axis is the difference of the chiral condensate between non-zero and zero anisotropy. Interestingly, this quantity is negative for small enough but nonzero anisotropy. This means that the anisotropy has the same qualitative effect on chiral symmetry breaking as a magnetic field, leading us to conjecture that IMC is a more general phenomenon related to anisotropy in general, not specifically magnetic fields.