It is known that spontaneously broken gauge theories are the only renormalizable theories of massive spin-one particles with mass dimension less than or equal to 4. This paper describes a search for renormalizable interactions with higher mass dimension. Specifically, we examine the high-energy behavior of a class of models which involve field-strength interactions. Power counting shows that the high-energy behavior of these models is no worse than the naively estimated high-energy behavior of a gauge theory in the $U$ gauge. Therefore, there may be a "soft" symmetry-breaking mechanism (for instance, a soft divergence of an antisymmetric tensor current) which enforces renormalizable high-energy behavior in the same way that spontaneously broken gauge invariance guarantees the renormalizability of gauge theories. This hope is supported by the existence of "gauge theories" of strings, which describe analogous interactions of strings and field strengths. Unfortunately, this idea is tarnished by explicit calculations in which renormalizability is imposed in the form of unitarity bounds. These unitarity bounds imply that all possible field-strength couplings must be zero and that the remaining interactions describe a spontaneously broken gauge theory. Thus this result supports an earlier conjecture that gauge theories are the only renormalizable theories of massive vector bosons.

• Received 8 April 1976

DOI:https://doi.org/10.1103/PhysRevD.14.465