Metric-Like Formulation Of the Spin-Three Gravity In Three Dimensions
Zhi-Qiang Guo

TL;DR
This paper reformulates three-dimensional spin-3 gravity from a Chern-Simons framework to a metric-like Einstein-Cartan theory, revealing a duality and coupling with higher-spin matter fields.
Contribution
It introduces a metric-like formulation of spin-3 gravity in three dimensions, connecting Chern-Simons theory with Einstein-Cartan theory and identifying a duality transformation.
Findings
Reformulation of spin-3 gravity as Einstein-Cartan theory
Identification of a duality-like transformation
Coupling of higher-spin matter fields
Abstract
We provide a metric-like formulation of the spin-3 gravity in three dimensions. It is shown that the Chern-Simons formulation of the spin-3 gravity can be reformulated as a Einstein-Cartan-Sciama-Kibble theory coupled with the higher-spin matter fields. A duality-like transformation is also identified from this metric-like formulation.
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