Mass generation for Self-dual Gauge Fields via Topologically Coupling

TL;DR

This paper investigates how self-dual two-form gauge fields acquire mass through topological coupling with a three-rank antisymmetric field, revealing different mechanisms depending on the Lagrangian formulation.

Contribution

It analyzes various non-covariant Lagrangians to demonstrate different mass generation mechanisms for self-dual gauge fields via topological coupling.

Findings

Massive self-dual two-form field equations resemble Klein-Gordon form.

The three-rank antisymmetric field can be eliminated or retained based on the formulation.

Different Lagrangians lead to distinct mass generation mechanisms.

Abstract

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 $\partial^2 B^{ab}+m^2B^{ab}=0$ 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.