On the continuum limit of spin foams: graviton dynamics and area metric induced corrections

Abstract

The semi-classical limit of spin foams leads to the Area Regge action. It was long thought that this action leads to flatness and does, in particular, not allow for propagating gravitons. I will present the first systematic studies of the continuum limit of the Area Regge action, using different versions of regular hypercubic lattices. These studies have shown that the Area Regge action does in its continuum limit, lead to leading order to general relativity, and thus to propagating gravitons. The higher order corrections depend on the choice of triangulation for the hypercubic lattice. However, there seems to be a preferred choice, for which the Area Regge action is not singular. In this case the correction term approximates the square of the Weyl curvature tensor, and can be interpreted to arise from an area metric dynamics. We therefore conjecture that the continuum limit of spin foams is described by an area metric theory.