Gravitational instantons and moduli spaces in topological two-form gravity

Abstract

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual two-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for a cosmological constant A # 0 case and an Einstein-Kahlerian manifold with the vanishing real first Chern class for A = 0. In the A # 0 case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for A = 0 which are related to Plebansky's heavenly equations.PACS number(s): 04.50.th, 04.20.Jb

Cosmic-rays and diffuse γ-rays: Spatial gradients of Galactic parameters

“…Fifth, we checked the spatial distributions in ðl; bÞ for two energy ranges, [0.5, 1], [1,2], (Figs. 13 and 14), and the shape of the spread in both l and b is satisfactorily reproduced by adopting an appropriate choice of the average scale heights, r and z.…”

“…Comparison of the present empirical formula with the experimental data on (a) inelastic cross-section in p-p collisions, and (b) total production cross-section of c's. For experimental data, see Paper IV and references therein, and see also Abe et al [2] for CDF, Amos et al [4] for E710 in (a), and Stecker [61] for the data (filled circles) in (b).…”

“…In Fig. 13, we plot EGRET data on the longitudinal distributions for two energy ranges, (a) E c = [0.5, 1] GeV, (b) [1,2] GeV with jbj 6 5 , together with the numerical curves for three radial scale heights, r ¼ 30; 40, and 60 kpc, each fixed to n = 0.832 H atoms cm À3 and z ¼ 500 pc, which are obtained by combining our p -induced c's with those induced by EB and IC (see Fig. 10).…”

Luminosity measurement in the interaction regions of the LHC using proton–proton collision multiplicities

“…Of particular importance is resolution on the z 0 impact parameter. 2 In order to distinguish different pp collisions within the same bunch crossing, we need the resolution on z 0 to be smaller than the typical distance between adjacent interactions. For charged tracks with p T ¼ 500 MeV=c produced in the central tracking region of the ATLAS Inner Detector, the resolution on the z 0 impact parameters is found to be sðz 0 Þ % 200 mm [9].…”

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