Classification of Subsystems for Local Nets with Trivial Superselection Structure

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed point net under a compact group action on one component in a suitable tensor product decomposition of F. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.Comment: 31 pages, LaTe

Conformal nets and KK-theory

Given a completely rational conformal net A on the circle, its fusion ring acts faithfully on the K_0-group of a certain universal C*-algebra associated to A, as shown in a previous paper. We prove here that this action can actually be identified with a Kasparov product, thus paving the way for a fruitful interplay between conformal field theory and KK-theory

Structure and Classification of Superconformal Nets

We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by considering the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2.Comment: 49 pages. Section 8 has been removed. More details concerning the diffeomorphism covariance are give

Rock mass characterization coupled with seismic noise measurements to analyze the unstable cliff slope of the Selmun Promontory (Malta)

In the Mediterranean area, cliff slopes represent widespread high-risk landforms as they are highly frequented touristic places often interested by landslide processes. Malta represents a significant case study as several cliffs located all around the island are involved in instability processes, as evidenced by wide block-size talus distributed all along the coast line. These diffused instabilities are related to the predisponding geological setting of Malta Island, i.e. the over-position of grained limestone on plastic clay deposits, that induces lateral spreading phenomena associated to falls and topples of different-size rock blocks and is responsible for a typical landscape with stable plateau of stiff rocks bordered by unstable cliff slopes. The ruins of Gƫajn ƪadid Tower, the first of the thirteen watchtowers built in 1658 by the Gran Master Martin de Redin, stand out in the Selmun area. Currently the safety of this important heritage site, already damaged by an earthquake on October 12th 1856, is threaten by a progressive moving of the landslide process towards the stable plateau area. During autumn 2015, a field campaign was realized to characterize the jointed rock mass. A detailed engineering-geological survey was carried out to reconstruct the geological setting and to define the mechanical properties of the rock mass. Based on the surveyed joint spatial distribution, 58 single-station noise measurements were deployed to cover both the unstable zone and the stable area. The obtained 1-hour records were analyzed in the frequency domain for associating vibrational evidences to different instability levels, i.e. deriving the presence of already isolated blocks by the local seismic response. The here presented results can be a useful contribute to begin to asses defense strategies for the Selmun Promontory, in the frame of managing the landslide risk in the study area and preserving the local historical heritage

From vertex operator algebras to conformal nets and back

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local vertex operator algebra V a conformal net A_V acting on the Hilbert space completion of V and prove that the isomorphism class of A_V does not depend on the choice of the scalar product on V. We show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W\mapsto A_W gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of A_V. Many known examples of vertex operator algebras such as the unitary Virasoro vertex operator algebras, the unitary affine Lie algebras vertex operator algebras, the known c=1 unitary vertex operator algebras, the moonshine vertex operator algebra, together with their coset and orbifold subalgebras, turn out to be strongly local. We give various applications of our results. In particular we show that the even shorter Moonshine vertex operator algebra is strongly local and that the automorphism group of the corresponding conformal net is the Baby Monster group. We prove that a construction of Fredenhagen and J\"{o}rss gives back the strongly local vertex operator algebra V from the conformal net A_V and give conditions on a conformal net A implying that A= A_V for some strongly local vertex operator algebra V.Comment: Minor correction

Transparent and efficient shared-state management for optimistic simulations on multi-core machines

Traditionally, Logical Processes (LPs) forming a simulation model store their execution information into disjoint simulations states, forcing events exchange to communicate data between each other. In this work we propose the design and implementation of an extension to the traditional Time Warp (optimistic) synchronization protocol for parallel/distributed simulation, targeted at shared-memory/multicore machines, allowing LPs to share parts of their simulation states by using global variables. In order to preserve optimism's intrinsic properties, global variables are transparently mapped to multi-version ones, so to avoid any form of safety predicate verification upon updates. Execution's consistency is ensured via the introduction of a new rollback scheme which is triggered upon the detection of an incorrect global variable's read. At the same time, efficiency in the execution is guaranteed by the exploitation of non-blocking algorithms in order to manage the multi-version variables' lists. Furthermore, our proposal is integrated with the simulation model's code through software instrumentation, in order to allow the application-level programmer to avoid using any specific API to mark or to inform the simulation kernel of updates to global variables. Thus we support full transparency. An assessment of our proposal, comparing it with a traditional message-passing implementation of variables' multi-version is provided as well. © 2012 IEEE

N=2 superconformal nets

We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is much richer. There are naturally associated nets of spectral triples and the JLO cocycles separate the Ramond sectors. We construct the N=2 superconformal nets of von Neumann algebras in general, classify them in the discrete series c<3, and we define and study an operator algebraic version of the N=2 spectral flow. We prove the coset identification for the N=2 super-Virasoro nets with c<3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.Comment: 42 pages. Final version to be published in Communications in Mathematical Physic

8. Book Reviews

Reviews of Coyer and Shuttleton (eds.), Scottish Medicine and Literary Culture, 1726-1832, Rodopi 2014; Poggi, L’anima e il cristallo. Alle radici dell’arte astratta, 2014.

Gravitational-wave extraction from neutron-star oscillations

We compare different gravitational-wave extraction methods used in three-dimensional nonlinear simulations against linear simulations of perturbations of spherical spacetimes with matter. We present results from fully general-relativistic simulations of a system composed by an oscillating and non-rotating star emitting gravitational radiation. Results about the onset of non-linear effects are also shown