Emergence of General Relativity from Cosmological Constant Via Ghost Condensation

Abstract

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 $R = 0$ \`{a} la BRST formalism, and see that the condensation of the Faddeev-Popov ghosts, $\langle \bar c c \rangle \neq 0$ 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.