From area metric backgrounds to the cosmological constant and corrections to the Polyakov action

Area metrics and area metric backgrounds provide a unified framework for quantum gravity. They encode physical degrees of freedom beyond those of a metric. These non-metric degrees of freedom must be suppressed by a potential at sufficiently high energy scales to ensure that in the infrared regime classical gravity is recovered. On this basis, we first study necessary and sufficient algebraic conditions for an area metric to be induced by a metric. Second, we consider candidate potentials for the area metric and point out a possible connection between the reduction of area metric geometry to metric geometry on the one hand, and the smallness of the cosmological constant on the other. Finally, we consider modifications of the Nambu-Goto action for a string, from a metric background to an area metric background. We demonstrate that area metric perturbations introduce an interaction corresponding to a singular vertex operator in the classically equivalent Polyakov action. The implications of these types of vertex operators for the quantum theory remain to be understood.