Narrow Results

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).