Mass generation for Self-dual Gauge Fields via Topologically Coupling

We study the mass generation of self-dual two form gauge field by topologically coupling it to the three rank anti-symmetric field. We use the various non-covariant Lagrangian of self-dual two form to perform the analysis and find that the field equation of massive self-dual two form gauge field may be described by ${\mathrm{\partial }}^2{B}^{ab}+m^2{B}^{ab}=0$ or $\partial_c (F^{cab}-\tilde F^{cab})+m^2B^{ab}=0$. We also find that, depending on the formulation of self-dual two form gauge field, the three rank anti-symmetric field may or may not be totally eliminated. Thus the different Lagrangian will show different mass generation mechanisms.