Ambiguities in the Seiberg-Witten Map and Emergent Gravity

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.

10 pages, typos corrected

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• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
• An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories