  The conformal version of the antisymmetric second-order tensor field in four
spacetime dimensions does not have gauge invariance extensively discussed in
the literature for more than half a century. Our first observation is that,
when coupled to fermions, only the conformal version provides renormalizability
of the theory at the one-loop level. General considerations are supported by
the derivation of one-loop divergences in the fermionic sector, indicating good
chances for asymptotic freedom. The arguments concerning one-loop
renormalizability remain valid in the presence of self-interactions and the
masses for both fermion and antisymmetric tensor fields. In the flat spacetime
limit, regardless of the conformal symmetry has gone, there is an expectation
to meet renormalizability in all loop orders.

High Energy Physics - Theory;General Relativity and Quantum Cosmology