f−gversion of theSL(6,C)gauge theory

The recently proposed $\mathrm{SL}\mathrm{}(6,C)\mathrm{}$ gauge-invariant theory describing a nonet of tensor mesons ($f$) interacting with hadrons is written in a generally covariant formulation. Assuming that leptons interact directly with gravitons ($g$), a generally covariant as well as $\mathrm{SL}\mathrm{}(6,C)\mathrm{}$ gauge-invariant $f-g$ mixing term is introduced to describe the gravitational interaction of hadrons as well as to provide masses for the SU(3)-octet $f$'s and for a singlet mixture of the $f$ and $g$ fields. The gauge symmetries are broken spontaneously and it is shown that a second orthogonal combination of $f-g$ fields remains massless, representing "true" gravity.