Duality Covariant Formulation of Extended Supergravity: Central Charges,BPS States and Black-Hole Entropy

In these lectures we give a geometrical formulation of N-extrended supergravities which generalizes N = 2 special geometry of N = 2 theories. In all these theories duality symmetries are related to the notion of “flat symplectic bundles” and central charges may be defined as “sections” over these bundles. Attractor points giving rise to “fixed scalars” of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.     

Semi-symmetric Lorentzian hypersurfaces in Lorentzian space forms

In the present paper, we shall investigate and classify Lorentzian hypersurfaces in Lorentzian space forms satisfying some curvature conditions. We shall focus especially on semi-symmetric Lorentzian hypersurfaces. Those of constant curvature and those so-called “good” are explicitly described and classified. We shall also classify Einstein–Lorentzian hypersurfaces.     

Leibniz' principle,general relativity,and the observational dominance of euclidean geometry

Leibniz' principle and the observational dominance of Euclidean geometry suggest a huge cosmological constant in Einstein's field equations and a correspondingly huge negative “vacuum” density. This theory lends support to renormalization procedures in quantum electrodynamics and to the view that the interactions we “observe” are fluctuations of the “vacuum state” interpreted as a Fermi sea. Einstein's “preferred” equations, with A=0, are recovered. “Empty” space has no metric geometry at all.     

Inclusive projectile fragmentation in the spectator model

Grazing-angle singles spectra for projectile fragments from nuclear collisions exhibit a broad peak centered near the beam velocity, suggesting that these observed fragments play only a “spectator” role in the reaction. Using only this spectator assumption (but not DWBA), we find that a “prior form” formulation of the reaction leads, via closure, to a 〈ψ∥W∥ψ〉-type estimate of the inclusive spectator spectrum, thus relating it to the reaction cross section for the “participant” with the target. We show explicitly that this expression includes an improved multi-channel version of the Udagawa-Tamura formula for the “breakup-fusion” or incomplete-fusion cross section, and identifies it as the fluctuation part of the participant-target reaction cross section. A Glauber-type estimate of the distorted wave functions which enter clearly shows how the width of the peak in the spectator spectrum arises from the “Fermi motion” within the projectile, as in the simpler Serber model, but is modified by the “overlap geometry” of the collision.     

Quantum bit threads of MERA tensor network in large c limit

The Ryu-Takayanagi (RT) formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena. The recent reinterpretation of this formula in terms of a set of “bit threads” is an interesting effort in understanding holography. In this study, we investigate a quantum generalization of the “bit threads” based on a tensor network, with particular focus on the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large c limit, isometries of the MERA can be regarded as “sources” (or “sinks”) of the information flow, which extensively modifies the original picture of bit threads by introducing a new variable ρ: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large c limit implies that classical gravity can emerge from the information flow.     

Stability of the Thin-Shell Schwarzschild-Ellis Wormhole

We investigate the stability regions of the thin-shells obtained by gluing the exterior Schwarzschild vacuum with two distinct classes of Ellis wormholes, one with zero and the other with nonzero total mass. Using the new concepts of thin-shell “mass” and of “external force” discovered recently by Garcia, Lobo and Visser, we shall apply their method to the explicit cases where some of the energy conditions in the bulk (on two sides) are violated. The stability regions are analyzed and the energetics is briefly discussed. Remarkably, we find that the stability zones are quite similar although the classes of Ellis wormholes are different. By the present examples, we confirm that the stability zones indicated by the force constraint (involving Φ and its derivatives) are more complete but restrictive than those from the mass constraint (not involving Φ).