Ambiguities in the Seiberg-Witten Map and Emergent Gravity

TL;DR

This paper investigates ambiguities in the Seiberg-Witten map within emergent gravity, showing how they affect the metric and scalar fields, and derives an exact map beyond linear approximation.

Contribution

It clarifies how gauge and field redefinitions influence emergent gravity metrics and introduces an exact Seiberg-Witten map beyond linear order.

Findings

Ambiguities can be removed by gauge transformation or field redefinition.

Field redefinition affects the emergent metric and non-minimal couplings.

Dispersion relations remain unaffected by metric ambiguities.

Abstract

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. Even though the metric depends on the ambiguity we show that the dispersion relation does not present any sign of it. A proposal for an exact Seiberg-Witten map is used to derive the full metric going beyond the linearized limit.