Two-measure theory with third-rank antisymmetric tensor for local scale symmetry breaking

We present a new mechanism of local scale symmetry breaking based on the scalar density Φ≡(1/3!)ϵμνρσ∂μAνρσ≡(1/4!)ϵμνρσFμνρσ(0) with an independent third-rank tensor Aμνρ, which replaces the scalar density Φ≡ϵμνρσϵabcd(∂μφa)(∂νφb)(∂ρφc)(∂σφd) used in "two-measure theory." We apply this function both to globally and locally scale-invariant systems. For local scale invariance, we modify Fμνρσ(0) by a certain Chern-Simons term, based on the recently developed tensor-hierarchy formulation. For a locally scale-invariant system with multiple scalars, the minimum value of the potential is realized at exactly zero value, while local scale invariance is broken by some nonzero vacuum expectation values: σi 0, Fmnrs=f0ϵmnrs≠0. For these values, the cosmological constant is maintained to be zero, despite the broken local scale invariance.