Renormalisation Group, Quantum Critical Points, Inflation And Ads/Cft, Anti–De Sitter Space/Conformal-Field-Theory Correspondence, Heavy Quark Jets In Anti–De Sitter Space/Conformal Field Theory, Holographic Entanglement Entropy, Lifshitz Topological Blac

K.N.P. Kumar, C.J. Prabhakara, S.K. Narasimha Murthy, B.J. Gireesha


Starting with the conformal symmetries of Euclidean space, Jeffrey S Hazboun and James T Wheeler construct a manifold where time manifests as a part of the geometry. Though there is no matter present in the geometry studied here, geometric terms analogous to dark energy and dark matter appear when write down the Einstein tensor. Specifically, the quotient of the conformal group of Euclidean four-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric. Jeffrey S Hazboun and James T Wheeler show that the general solution possesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, despite the Euclidean starting point. Using an orthonormal frame adapted to the phase space properties, authors also find two new tensor fields not present in Riemannian geometry. The first is a combination of the Weyl vector with the scale factor on the metric, and determines the timelike directions on the submanifolds. The second comes from the components of the spin connection, symmetric with respect to the new metric. Though this field comes from the spin connection, it transforms homogeneously. Finally, they show that in the absence of Cartan curvature and sources, the configuration space has geometric terms equivalent to a perfect fluid and a cosmological constant.

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