Schrödinger connection with selfdual nonmetricity vector in 2+1 dimensions

Abstract

We present a three-dimensional metric affine theory of gravity whose field equations lead to a connection introduced by Schrödinger many decades ago. Although involving nonmetricity, the Schrödinger connection preserves the length of vectors under parallel transport, and appears thus to be more physical than the one proposed by Weyl. By considering solutions with constant scalar curvature, we obtain a self-duality relation for the nonmetricity vector which implies a Proca equation that may also be interpreted in terms of inhomogeneous Maxwell equations emerging from affine geometry.

5 pages

References in corpus (3)

• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Einstein--Weyl Spaces and Near-Horizon Geometry
• Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces

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• New Torsional Deformations of Locally AdS${}_3$ Space
• Warm Inflation in $f(Q)$ gravity
• Metric-Affine Myrzakulov Gravity Theories
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• Cosmological test of a length-preserving biconnection gravity