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

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arxiv 2408.07159 v2 pith:RKHL2FXM submitted 2024-08-13 hep-th gr-qchep-ph

Cezar Condeescu , Andrei Micu This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords weylgroupgaugegravitynon-metricityquadratictheorytorsion
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. World-Line Actions in Weyl Geometry

    hep-th 2026-07 accept novelty 6.0 of 10

    A dimensionless Weyl-invariant additive world-line action exists for time-like particles in Weyl geometry, but proper time cannot be defined until scale symmetry breaks.

  2. Weyl gauge symmetry at LIGO-Virgo-KAGRA

    gr-qc 2026-07 conditional novelty 6.0 of 10

    In Weyl quadratic gravity linearized around de Sitter space, gravitational waves carry two tensor modes plus two transverse vector modes from the Weyl gauge field, with no scalar modes.

  3. Conformal geometry as a gauge theory of gravity: covariant equations of motion & conservation laws

    hep-th 2024-12 conditional novelty 6.0 of 10

    The most general Weyl-quadratic-gravity action yields manifestly gauge-covariant equations of motion, with energy-momentum and Weyl-current conservation holding in both the Weyl and Riemannian pictures.

  4. The fall and the rise of Weyl gauge theory

    gr-qc 2026-04 unverdicted novelty 5.0 of 10

    Weyl quadratic gauge gravity is anomaly-free, breaks via Stueckelberg to Einstein-Hilbert plus positive Lambda, and is the leading order of a regulator-free WDBI action that can include the SM.

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