Weylambient geometries
Abstract
Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the FeffermanGraham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weylambient metric motivated by the WeylFeffermanGraham (WFG) gauge. From a topdown perspective, we show that the Weylambient space as a pseudoRiemannian geometry induces a codimension2 Weyl geometry. Then, from a bottomup perspective, we start from promoting a conformal manifold into a Weyl manifold by assigning a Weyl connection to the principal R_{+}bundle realizing a Weyl structure. We show that the Weyl structure admits a welldefined initial value problem, which determines the Weylambient metric. Through the Weylambient construction, we also investigate Weylcovariant tensors on the Weyl manifold and define extended Weylobstruction tensors explicitly.
 Publication:

Nuclear Physics B
 Pub Date:
 June 2023
 DOI:
 10.1016/j.nuclphysb.2023.116224
 arXiv:
 arXiv:2301.06628
 Bibcode:
 2023NuPhB.99116224J
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 42 pages, 1 figure