Dynamically emergent gravity from hidden local Lorentz symmetry

Abstract

Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent.