Emergence of general relativity from cosmological constant via ghost condensation

We show that starting with a cosmological constant in a curved space-time, the Einstein–Hilbert term of general relativity is generated through a ghost condensation. We fix Weyl symmetry, or equivalently local scale symmetry by a gauge condition [Formula: see text] à la BRST formalism, and see that the condensation of the Faddeev–Popov ghosts, [Formula: see text] leads to a generation of the Einstein–Hilbert action of general relativity. This dynamical mechanism of symmetry breakdown for a global scale symmetry is new in the sense that the reduction of fermionic degrees of freedom effectively leads to a generation of bosonic degrees of freedom. We also discuss this mechanism from the viewpoint of the problem of a bound state, and show that asymptotic fields corresponding to the bound states are “confined” to the unphysical Hilbert space.