Antisymmetric Tensor Field and Cheshire Cat Smile of the Local Conformal Symmetry

TL;DR

This paper investigates the conformal antisymmetric tensor field in four dimensions, revealing its unique renormalizability when coupled to fermions and suggesting potential asymptotic freedom, with implications for quantum field theory consistency.

Contribution

It demonstrates that the conformal antisymmetric tensor field coupled to fermions is one-loop renormalizable and likely asymptotically free, a novel insight in the study of gauge invariance and conformal symmetry.

Findings

One-loop divergences support renormalizability.

Coupling to fermions is essential for renormalizability.

Potential for all-order renormalizability in flat spacetime.

Abstract

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.