Abstract
A homogeneous part of the Seiberg-Witten gauge equivalence relation for gauge fields can lead to solutions that involve matter fields in such a way that the gauge equivalence and the dimensional and index structures are preserved. In particular, we consider scalar fields coupled to U(1) gauge fields. The matter fields appear non-linearly in the map. As an application, we analyze the implication of this ambiguity to emergent gravity at the first order in noncommutative parameter and show that the new ambiguity restores the possibility of conformal coupling of real scalar density field that is coupled non-minimally to the emergent gravity induced by gauge fields -- a possibility that is strictly not allowed if we consider only the already known ambiguity in the Seiberg-Witten map.
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