XIV Bolyai–Gauss–Lobachevsky Conference (BGL–2026): Non-Euclidean Geometry in Modern Physics and Mathematics

Weyl-Dirac-Born-Infeld action for quantum gravity

16 Sept 2026, 12:00

30m

Main Building (Babeș-Bolyai University, Cluj-Napoca, Romania)

Speaker

Dumitru Ghilencea (Horia Hulubei National Institute of Physics and Nuclear Engineering (RO))

Description

Weyl conformal geometry is the natural underlying geometry of (local) gauge theories of the Weyl group (of dilatations and Poincare symmetry), such as Weyl quadratic gravity (WQG) and its generalisation, Weyl-Dirac-Born-Infeld
action (WDBI). The WDBI action is well-defined in arbitrary d dimensions with no need for a UV regulator scale/field. A series expansion of WDBI action (in dimensionless coupling) recovers in the leading order a Weyl gauge invariant (geometrically regularised!) version of d=4 Standard Model (SM) and WQG. Riemannian geometry, Einstein-Hilbert action and a cc>0 are recovered in the Stueckelberg broken phase of Weyl gauge symmetry. Interestingly, Weyl geometry can also be seen as
Riemannian geometry of a (Weyl gauge invariant) non-local dressed metric (by Wilson line of dilatations), at the ”cost” of UV non-commutativity in the vector space of observables, (due to Weyl flux). Quantum non-locality, in particular quantum entanglement, and UV non-commutativity are then artefacts of ”viewing” Weyl geometry from (our-world of) Riemannian geometry of Weyl gauge invariant fields/observables and are evidence of Weyl gauge symmetry. Based on e-Prints: 2508.10959 and 2606.08080.