Studying the quark gap equation at finite temperature, magnetic field and different numbers of flavor and color numbers

In recent years, a momentum-independent symmetry preserving vector-vector contact interaction has been used to provide exploratory studies in QCD. It helps calculate different static and dynamic observables of all mesons and baryons. In this work, we revisit how the quark gap equation is affected by changing the number of quark colors and/or flavors, or by placing quarks in a thermal bath in the presence of an external magnetic field. In particular, we describe how the phenomenon of magnetic catalysis and its inverse can be studied.