Where does the scale originate from in going from pure R2 gravity to the equivalent Einstein gravity?

Speaker: Ariel Edery

Higher-derivative gravity theories have the well-known problem of not being unitary. However, there is one exception: pure R² gravity (R² gravity alone). Not only is it unitary but it has recently been shown by a few groups that this theory is equivalent to Einstein gravity with a non-zero cosmological constant minimally coupled to a massless scalar field. The original theory is scale-invariant but the equivalent Einstein theory is not. A crucial question is ``where does the scale originate from?" We point out that the conformal transformation that is performed in going from R² to Einstein gravity naturally selects a background spacetime with non-zero Ricci scalar R. This vacuum state does not preserve the symmetry of the action and the scale symmetry is spontaneously broken. We identify the massless scalar field as the Nambu-Goldstone boson associated with the broken symmetry.