Inducing the cosmological constant from five-dimensional Weyl space

Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity

By extending the recent analysis of arXiv:2203.12203 for ${\mathcal{N}}=2$ conformal supergravity in four dimensions, we define new hyper-dilaton Weyl multiplets for five-dimensional ${\mathcal{N}}=1$, and six-dimensional ${\mathcal{N}}=(1,0)$ conformal supergravities. These are constructed by coupling the five- and six-dimensional standard Weyl multiplets to on-shell hypermultiplets and reinterpreting the systems as new multiplets of conformal supergravity. In the five-dimensional case, we also construct a new hyper-dilaton Poincaré supergravity by coupling to an off-shell vector multiplet co…

Refinements of the Weyl tensor classification in five dimensions

We refine the null alignment classification of the Weyl tensor of a five-dimensional spacetime. The paper focusses on the algebraically special alignment types {\bf {N}}, {\bf {III}}, {\bf {II}} and {\bf {D}}, while types {\bf {I}} and {\bf {G}} are briefly discussed. A first refinement is provided by the notion of spin type of the components of highest boost weight. Second, we analyze the Segre types of the Weyl operator acting on bivector space and examine the intersection with the spin type classification. We present a full treatment for types {\bf {N}} and {\bf {III}}, and illustrate the c…

Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces

We show that the horizon geometry for supersymmetric black hole solutions of minimal five-dimensional gauged supergravity is that of a particular Einstein-Cartan-Weyl (ECW) structure in three dimensions, involving the trace and traceless part of both torsion and nonmetricity, and obeying some precise constraints. In the limit of zero cosmological constant, the set of nonlinear partial differential equations characterizing this ECW structure reduces correctly to that of a hyper-CR Einstein-Weyl structure in the Gauduchon gauge, which was shown by Dunajski, Gutowski and Sabra to be the horizon g…

Nonexistence of Petrov type III Space-Times on which Weyl's Neutrino Equation or Maxwell's Equations satisfy Huygens' Principle

Extending previous results we show that there are no Petrov type III space-times on which either the Weyl neutrino equation or Maxwell's equations satisfy Huygens' principle. We prove the result by using Maple's NPspinor package to convert the five-index necessary condition obtained by Alvarez and Wunsch to dyad form. The integrability conditions of the problem lead to a system of polynomial equations. We then apply Maple's grobner package to show that this system has no admissible solutions.

Segal-Bargmann变换与Meixner类正交多项式相关的广义Weyl代数

Segal-Bargmann transforms and generalized Weyl algebras associated with the Meixner class of orthogonal polynomials

本文研究Meixner类正交多项式相关的广义Segal-Bargmann变换及广义Weyl代数的正常排列方法。

Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions

Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalises the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field e…