Entropic order parameters in weakly coupled gauge theories

The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.

Local Energy Systems in Iraq: Neighbourhood Diesel Generators and Solar Photovoltaic Generation

Iraqis experience interruptions of the public electricity supply of up to 18 hours a day. In response, private entrepreneurs and the Local Provincial Councils (LPCs) have installed an estimated 55,000–80,000 diesel generators, each rated typically between 100 and 500 kVA. The generators supply neighbourhoods through small, isolated distribution networks to operate lighting, fans and small appliances when power is not available from the public supply. A single radial live conductor connects each customer to the generator and payment for the electricity is based on a monthly charge per ampere. The operation and regulation of the neighbourhood diesel generator networks was reviewed through a comprehensive literature survey, site visits and interviews conducted with local operators and assemblers of the generator sets. The electricity is expensive, the generators can only supply small loads, have considerable environmental impact and the unusual single wire distribution practice is potentially hazardous. However, the use of the generators is likely to continue in the absence of any alternative electricity supply. The diesels and networks are poorly regulated and there is scope to enforce existing standards and develop a new standard to address the hazards of the connection practice. The chapter goes on to assess the possibilities of using small photovoltaic systems for power generation in Iraq.

Value Configurations for Data and Connectivity Solutions in Digitalized Future Factories

The ongoing Industry 4.0 transformation places significant pressures on how businesses create and capture value. Technological advancements such as next-generation mobile communications are reshaping the business ecosystem of Industry 4.0, resulting in emerging business opportunities for new players, such as local operators, to collaborate and compete with mobile communications companies that are implementing I4.0. These changes raise the need to explore emerging business opportunities concerning the digitalization of future factories. New data and connectivity services are introduced to serve the needs of rapidly increasing machine-type communications that rely on connectivity, primarily through the fifth generation (5G) mobile solutions provided by local operators. Thus, this paper outlines the potential value configurations for data and connectivity solutions by identifying, matching, and bridging the utilizable resources and addressable needs within the factory processes. The research applies an exploratory approach and uses the Gioia method to analyze qualitative data of a single case. The study follows the connectivity-content-context-commerce typology (4C) of Internet business models to structure, analyze, and classify the identified needs and resources in future factories from the perspective of the local operator. The findings show that the content layer of 4C business model typology is the most dominant among data and connectivity-based needs and resources of future factories. The paper contributes by presenting four alternative value configurations for digitalization for local operators in the future factory context: the product, component, platform, and complementary businesses. The results suggest content- and context-specific businesses carries foremost business potential for local operators, however quantitative validation will bring fruitful research avenues. Multiple case studies and different data collection methods may also be considered in future studies.

Kernel-independent adaptive construction of $$\mathcal {H}^2$$-matrix approximations

A method for the kernel-independent construction of $$\mathcal {H}^2$$ H 2 -matrix approximations to non-local operators is proposed. Special attention is paid to the adaptive construction of nested bases. As a side result, new error estimates for adaptive cross approximation (ACA) are presented which have implications on the pivoting strategy of ACA.

The form of locally defined operators in waterman spaces

A representation formula for locally defined operators acting between Banach spaces of continuous functions of bounded variation in the Waterman sense is presented. Moreover, the Nemytskij composition operators will be investigated and some consequences for locally bounded as well as uniformly bounded local operators will be given.

BiGONLight: light propagation with bi-local operators in Numerical Relativity

BiGONLight, Bilocal Geodesic Operators framework for Numerical Light propagation, is a new tool for light propagation in Numerical Relativity. The package implements the Bi-local Geodesic Operators formalism, a new framework for light propagation in General Relativity. With BiGONLight it is possible to extract observables such as angular diameter distance, luminosity distance, magnification as well as new real-time observables like parallax and redshift drift within the same computation. As a test-bed for our code we consider two exact cosmological models, the ΛCDM and the inhomogeneous Szekeres model, and a simulated dust universe. All our tests show an excellent agreement with known results.

Towards high-precision parton distributions from lattice QCD via distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

Bootstrapping quantum extremal surfaces. Part I. The area operator

Quantum extremal surfaces are central to the connection between quantum information theory and quantum gravity and they have played a prominent role in the recent progress on the information paradox. We initiate a program to systematically link these surfaces to the microscopic data of the dual conformal field theory, namely the scaling dimensions of local operators and their OPE coefficients. We consider CFT states obtained by acting on the vacuum with single-trace operators, which are dual to one-particle states of the bulk theory. Focusing on AdS3/CFT2, we compute the CFT entanglement entropy to second order in the large c expansion where quantum extremality becomes important and match it to the expectation value of the bulk area operator. We show that to this order, the Virasoro identity block contributes solely to the area operator.

Singular and Non-Singular Kernels Aspect of Time-Fractional Coupled Spring-Mass System

Dynamical behaviors of the time-fractional nonlinear model of the coupled spring-mass system with damping have been explored here. Fractional derivatives with singular and non-singular kernels are used to assess the suggested model. The fractional Adams-Bashforth numerical method based on Lagrange polynomial interpolation is applied to solve the system with non-local operators. Existence, Ulam-Hyers stability, and uniqueness of the solution are established by using fixed-point theory and nonlinear analysis. Further, the error analysis of the present method has also been included. Finally, the behavior of the solution is explained by graphical representations through numerical simulations.

A CFT distance conjecture

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.