Ambiguities in the Seiberg-Witten Map and Emergent Gravity

Understand

The theta expansion of the Seiberg-Witten map has ambiguities which can be removed by a gauge transformation and/or a field redefinition.

• In the context of emergent gravity such a field redefinition changes the emerging metric and requires the presence of non-minimal gravitational couplings.
• It also requires that a real scalar field becomes a scalar density and allows the introduction of a potential.
• We also find that the potential can have only one term and that a quartic interaction is not allowed.