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 Phi equivalent to (1/3!)epsilon(mu upsilon rho sigma) partial derivative(mu)A(upsilon rho sigma) with an independent third-rank tensor A(mu upsilon rho),which replaces the scalar density Phi equivalent to epsilon(mu upsilon rho sigma)epsilon(abcd)(partial derivative(mu)phi(a)) (partial derivative(upsilon)phi(b)) (partial derivative(rho)phi(c))(partial derivative(sigma)phi(d)) used in "two- measure theory." We apply this function both to globally and locally scale-invariant systems. For local scale invariance, we modify F-mu upsilon rho sigma((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: there exists <sigma(i)> not equal 0, there exists < F-mnrs > = f(0)epsilon(mnrs) not equal 0. For these values, the cosmological constant is maintained to be zero, despite the broken local scale invariance.