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

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### abstract

• We present a new mechanism of local scale symmetry breaking based on the scalar density $\mathrm{\ensuremath{\Phi}}\ensuremath{\equiv}(1/3!){\ensuremath{\epsilon}}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}{\ensuremath{\partial}}_{\ensuremath{\mu}}{A}_{\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}\ensuremath{\equiv}(1/4!){\ensuremath{\epsilon}}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}{F}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}^{(0)}$ with an independent third-rank tensor ${A}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$, which replaces the scalar density $\mathrm{\ensuremath{\Phi}}\ensuremath{\equiv}{\ensuremath{\epsilon}}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}{\ensuremath{\epsilon}}_{abcd}({\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\varphi}}^{a})({\ensuremath{\partial}}_{\ensuremath{\nu}}{\ensuremath{\varphi}}^{b})({\ensuremath{\partial}}_{\ensuremath{\rho}}{\ensuremath{\varphi}}^{c})({\ensuremath{\partial}}_{\ensuremath{\sigma}}{\ensuremath{\varphi}}^{d})$ used in two-measure theory.'' We apply this function both to globally and locally scale-invariant systems. For local scale invariance, we modify ${F}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}^{(0)}$ 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: $^{\ensuremath{\exists}}⟨{\ensuremath{\sigma}}_{i}⟩\ensuremath{\ne}0$, $^{\ensuremath{\exists}}⟨{F}_{mnrs}⟩={f}_{0}{\ensuremath{\epsilon}}_{mnrs}\ensuremath{\ne}0$. For these values, the cosmological constant is maintained to be zero, despite the broken local scale invariance.

### publication date

• March 6, 2017