Chiral Symmetry and Large Magnetic Fields

Abstract

Large magnetic fields exist in magnetars and are produced in off-central heavy-ion collisions. For the latter, field strengths are estimated to be comparable to strong interaction scales. This fact has motivated many studies of QCD physics in large magnetic fields, ranging from various model studies to lattice QCD computations. We provide a selective overview of results stemming from chiral perturbation theory. These results are based solely on the pattern of spontaneous and explicit symmetry breaking of QCD in a magnetic field; accordingly, they constitute low-energy theorems that must be satisfied in any approach. A few discrepancies with models and tension with lattice data are highlighted.