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arXiv · 2408.07159

The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity

Cezar Condeescu·Andrei Micu
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Abstract

In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a redefinition of the generators of the Weyl group. We present a generalisation of the torsion/non-metricity duality which includes, aside from the vector, also a traceless 3-tensor with two antisymmetric indices and vanishing skew symmetric part. A discussion of this relation in the case of minimally coupled matter fields is given. We further point out that a Rarita-Schwinger field can couple minimally to all the components of torsion and some components of non-metricity. Alongside we present the same gauge construction for the Poincar\'e and conformal groups. We show that even though the Weyl group is a subgroup of the conformal group, the gauge theory of the latter is actually only a special case of Weyl quadratic gravity.

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Cezar Condeescu, Andrei Micu. 2024-08-13. The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity. https://arxiv.org/abs/2408.07159

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