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Cosmic microwave background data shows the observable universe to be nearly flat, but leaves open the question of whether it is simply or multiply connected. Several authors have investigated whether the topology of a multiconnected hyperbolic universe would be detectable when 0.9<Ω<1. However, the possibility of detecting a given topology varies depending on the location of the observer within the space. Recent studies have assumed the observer sits at a favorable location. The present paper extends that work to consider observers at all points in the space, and (for given values of Ω_m and Ω_Λ and a given topology) computes the probability that a randomly placed observer could detect the topology. The computations show that when Ω=0.98 a randomly placed observer has a reasonable chance (~50%) of detecting a hyperbolic topology, but when Ω=0.99 the chances are low (<10%) and decrease still further as Ω approaches one.

It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero-mode quantum algebra in the presence of nontrivial topology.

We study inhomogeneities in the distribution of the excursion sets in the Cosmic Microwave Background (CMB) temperature maps obtained by the three years survey of the Wilkinson Microwave Anisotropy Probe (WMAP). At temperature thresholds |T| = 90 μK, the distributions of the excursion sets with over 200 pixels are concentrated in two regions, nearly at the antipodes, with galactic coordinates l = 94.7°, b = 34.4° and l = 279.8°, b = -29.2°. The centers of these two regions drift towards the equator when the temperature threshold is increased. The centers are located close to one of the vectors of ℓ = 3 multipole. The two patterns of the substructures in the distribution of the excursion sets are mirrored, with χ² = 0.7–1.5. There is no obvious origin of this effect in the noise structure of WMAP, and there is no evidence for a dependence on the galactic cut. Would this effect be cosmological, it could be an indication of an anomalously large component of horizon-size density perturbations, independent of one of the spatial coordinates, and/or of a non-trivial slab-like spatial topology of the Universe.

We study a class of topological black hole solutions in RSII braneworld scenario in the presence of a localized Maxwell field on the brane. Such a black hole can carry two types of charge, one arising from the extra dimension, the tidal charge, and the other from a localized gauge field confined to the brane. We find that the localized charge on the brane modifies the bulk geometry and in particular the bulk Weyl tensor. The bulk geometry does not depend on different topologies of the horizons. We present the temperature and entropy expressions associated with the event horizon of the braneworld black hole and by using the first law of black hole thermodynamics we calculate the mass of the black hole.

We describe the finite volume effects of CP-odd quantities, such as the neutron electric dipole moment and the anapole moment in the θ-vacuum, under different topological sectors. We evaluate the three-point Green's functions for the electromagnetic current in a fixed nontrivial topological sector in order to extract these CP-odd observables. We discuss the role of zero modes in the CP-odd Green's function and show that, in the quenched approximation, there is a power divergence in the quark mass for CP-odd quantities at finite volume.

An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered as a regularization of the Schwarzschild solution over a simply-connected manifold, which has a curvature singularity at the center. Spherically symmetric collapse of matter in ℝ⁴ may result in this nonsingular black-hole solution, if quantum-gravity effects allow for topology change near the center.

Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard Schwarzschild solution with a curvature singularity at the center. Spherically symmetric collapse of matter in ℝ⁴ may result in these nonsingular black-hole solutions, if quantum-gravity effects allow for topology change near the center or if nontrivial topology is already present as a remnant from a quantum spacetime foam.

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density $(n_0)$, the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise both to the long-standing “effective $g_A^{\ast }\approx 1$” in nuclear Gamow–Teller (GT) transitions at $\lesssim n_0$ and to the pseudo-conformal sound velocity $v_{\mathrm{\text{pcs}}}^2/c^2\approx 1/3$ at $\gtrsim 3n_0$. It is suggested that what has been referred to, since a long time, as “quenched $g_A$” in light nuclei reflects what leads to the dilaton-limit $g_A^{\mathrm{\text{DL}}}=1$ at near the (putative) infrared fixed point of scale invariance. These properties are confronted with the recent observations in GT transitions and in astrophysical observations.

In 1983, Donaldson shocked the topology world by using instantons from physics to prove new theorems about four-dimensional manifolds, and he developed new topological invariants. In 1988, Witten showed how these invariants could be obtained by correlation functions for a twisted N = 2 SUSY gauge theory. In 1994, Seiberg and Witten discovered dualities for such theories, and in particular, developed a new way of looking at four-dimensional manifolds that turns out to be easier, and is conjectured to be equivalent to, Donaldson theory.

This review describes the development of this mathematical subject, and shows how the physics played a pivotal role in the current understanding of this area of topology.

A non-trivial spatial topology of the Universe is a potentially observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological parameters. We show how one can use a possible circles-in-the-sky detection of the spatial topology of globally homogeneous universes to set constraints on the dark energy equation of state parameters.

Motivated by the study of soluble models of quantum field theory, we illustrate a new type of topological effect by comparing the constructions of canonical Klein–Gordon quantum fields on the two-dimensional de Sitter spacetime as opposed to its double covering. We show that while the commutators of the two fields coincide locally, the global topological differences make the theories drastically different. Many of the well-known features of de Sitter quantum field theory disappear. In particular, there is nothing like a Bunch–Davies vacuum. Correspondingly, even though the local horizon structure is the same for the two universes, there is no Hawking–Gibbons thermal state. Finally, there is no complementary series of fields.

QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the quark–gluon plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.

We explore the interplay between quantization, local commutativity and the analyticity properties of the two-point functions of a quantum field in a non trivial topological cosmological background in the example of the two-dimensional de Sitter manifold and its double covering. The global topological differences make the many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum and there are no $SL(2,R)$-invariant fields whose mass is less than 1/2.

The experiments at the Large Hadron Collider (LHC) rely upon a complex distributed computing infrastructure (WLCG) consisting of hundreds of individual sites worldwide at universities and national laboratories, providing about half a billion computing job slots and an exabyte of storage interconnected through high speed networks. Wide Area Networking (WAN) is one of the three pillars (together with computational resources and storage) of LHC computing. More than 5 PB/day are transferred between WLCG sites. Monitoring is one of the crucial components of WAN and experiments operations. In the past years all experiments have invested significant effort to improve monitoring and integrate networking information with data management and workload management systems. All WLCG sites are equipped with perfSONAR servers to collect a wide range of network metrics. We will present the latest development to provide the 3D force directed graph visualization for data collected by perfSONAR. The visualization package allows site admins, network engineers, scientists and network researchers to better understand the topology of our Research and Education networks and it provides the ability to identify nonreliable or/and nonoptimal network paths, such as those with routing loops or rapidly changing routes.

In this paper, we construct a class of quantum systems in a space continuum inspired by results from topological insulator physics. Instead of adding spin–orbit coupling terms suggested by time-reversal invariance as in conventional topological insulators, the terms $L\cdot S$ are determined using supersymmetry as a starting point. This procedure not only restricts the number of possible continuous topological insulators models, but also provides a systematic way to find new continuous topological insulators models. Some explicit quantum mechanical examples are discussed and applications to dark matter physics are also outlined.

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO(n) tensor (∂)^dh_αβ, which generally appears in the weak field expansion around the flat space: g_μν=δ_μν+h_μν. Making use of this representation, we explain (1) Generating function of graphs (Feynman diagram approach), (2) Adjacency matrix (Matrix approach), (3) Graphical classification in terms of "topology indices" (Topology approach), (4) The Young tableau (Symmetric group approach). We systematically construct the global SO(n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of ∂∂h-, and (∂∂h)²-invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).

In this work we propose a new procedure on how to extract global information of a space-time. We consider a space-time immersed in a higher dimensional space and formulate the equations of Einstein through the Frobenius conditions of immersion. Through an algorithm and implementation into algebraic computing system we calculate normal vectors from the immersion to find the second fundamental form. We make an application for a static space-time with spherical symmetry. We solve Einstein's equations in the vacuum and obtain space-times with different topologies.

It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes appear in General Relativity and how it leaves an observable footprint in space-time. In cosmology we show that such topological observable is the cosmic radiation produced by the acceleration of the universe. The cosmological constant is a very particular case which occurs when the expansion of the universe into the vacuum occurs only in the direction of the cosmic time flow.

We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.