QCD phase diagram in a constant magnetic background

Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at T = 0 is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalization scheme. A straightforward application of the quark-meson model and the NJL model leads to the prediction that the chiral transition temperature T-chi is increasing as a function of the magnetic field B. This is in disagreement with lattice results, which show that T-chi is a decreasing function of B, independent of the pion mass. The behavior can be understood in terms of the so-called valence and sea contributions to the quark condensate and the competition between them. We critically examine these ideas as well recent attempts to improve low-energy models using lattice input.

Automated summary

Magnetic catalysis refers to the enhancement of a condensate under the influence of an external magnetic field, a robust phenomenon in low-energy theories, QCD models, and lattice simulations. The quark-meson model serves as a specific example of magnetic catalysis but predicts different behavior compared to lattice results, particularly in terms of the chiral transition temperature T-chi as a function of the magnetic field B. The disagreement may be attributed to the interplay between valence and sea contributions to the quark condensate and ongoing attempts to improve low-energy models using lattice input.