Towards effective actions for the continuum limit of spin foams

Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to the continuum limit of spin foams are whether general relativity is reproduced and what type of corrections could emerge. As a central component for spin foam dynamics, recent results on the continuum limit of the Area Regge action suggest a close relation with actions for area metrics instead of a length metric. Inspired by these results, within the framework of modified Plebanski theory we construct a family of candidate actions for area metrics. These actions are expected to describe the continuum limit of spin foams and provide a starting point to explore phenomenological aspects of the large-scale dynamics of spin foams. More generally, they set the stage for exploring consequences of an enlargement of the configuration space for gravity from length to area metrics. The actions we construct lead to an effective action for the length metric, describing a non-local and ghost-free version of Einstein-Weyl gravity.