State-operator correspondence in celestial conformal field theory

The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.

Anomalous dimensions of monopole operators in scalar QED3 with Chern-Simons term

We study monopole operators with the lowest possible topological charge q = 1/2 at the infrared fixed point of scalar electrodynamics in 2 + 1 dimension (scalar QED3) with N complex scalars and Chern-Simons coupling |k| = N. In the large N expansion, monopole operators in this theory with spins $$ \mathrm{\ell}<O\left(\sqrt{N}\right) $$ ℓ < O N and associated flavor representations are expected to have the same scaling dimension to sub-leading order in 1/N. We use the state-operator correspondence to calculate the scaling dimension to sub-leading order with the result N − 0.2743 + O(1/N), which improves on existing leading order results. We also compute the ℓ2/N term that breaks the degeneracy to sub-leading order for monopoles with spins $$ \mathrm{\ell}=O\left(\sqrt{N}\right) $$ ℓ = O N .

On BPS strings in $$ \mathcal{N} $$ = 4 Yang-Mills theory

We study singular time-dependent $$ \frac{1}{8} $$ 1 8 -BPS configurations in the abelian sector of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory that represent BPS string-like defects in ℝ × S3 spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $$ \frac{1}{8} $$ 1 8 -BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global AdS5 × S5 that share supersymmetries with a class of dual-giant gravitons. For simple configurations, we demonstrate how to define a good variational problem and propose a regularization scheme that leads to finite energy and global charges on both sides of the holographic correspondence.

Joint State Composition Theorems for Public-Key Encryption and Digital Signature Functionalities with Local Computation

In frameworks for universal composability, complex protocols can be built from sub-protocols in a modular way using composition theorems. However, as first pointed out and studied by Canetti and Rabin, this modular approach often leads to impractical implementations. For example, when using a functionality for digital signatures within a more complex protocol, parties have to generate new verification and signing keys for every session of the protocol. This motivates to generalize composition theorems to so-called joint state (composition) theorems, where different copies of a functionality may share some state, e.g., the same verification and signing keys. In this paper, we present a joint state theorem which is more general than the original theorem of Canetti and Rabin, for which several problems and limitations are pointed out. We apply our theorem to obtain joint state realizations for three functionalities: public-key encryption, replayable public-key encryption, and digital signatures. Unlike most other formulations, our functionalities model that ciphertexts and signatures are computed locally, rather than being provided by the adversary. To obtain the joint state realizations, the functionalities have to be designed carefully. Other formulations proposed in the literature are shown to be unsuitable. Our work is based on the IITM model. Our definitions and results demonstrate the expressivity and simplicity of this model. For example, unlike Canetti’s UC model, in the IITM model no explicit joint state operator needs to be defined and the joint state theorem follows immediately from the composition theorem in the IITM model.

Comments on a state-operator correspondence for the torus

We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

Application of modified Asimov’s laws to the agent of home service robot using state, operator, and result (Soar)

This study aims to interpret and apply Asimov’s Three Laws of Robotics to home service robots. An agent is developed herein with the ability to focus its attention on human beings’ health, particularly the elderly and the diseased, by delivering food. The agent is developed on a cognitive agent architecture, state, operator, and result (Soar), to enable effective reasoning and decision-making skills. This study deals with basic home care services, such as food delivery and emergency response; therefore, common food care and emergency rules are newly proposed based on the priority values that correspond to a family’s circumstances and/or emergency levels. Asimov’s Three Laws are modified to aid the home service robot to follow a predetermined order in selecting a food item or recommending an alternative food item suitable for its user’s prevailing health condition. Experimental results confirm that reasoning and decision-making of the proposed agent are logically and ethically valid for a home service robot and ensure compliance with both the original and modified Asimov’s Three Laws.

Effect algebras with state operator

A state operator on effect algebras is introduced as an additive, idempotent and unital mapping from the effect algebra into itself. The definition is inspired by the definition of an internal state on MV-algebras, recently introduced by Flaminio and Montagna. We study state operators on convex effect algebras, and show their relations with conditional expectations on operator algebras.

AIRCRAFT OPERATION DEPENDING UPON THE UNCERTAINTY OF MAINTENANCE ALTERNATIVES

The paper considers the theoretical explanation and construction of some mathematical models of the aircraft operational process in reference to maintenance organizations preferred by aviation experts and aircraft operators. The uncertainty of such operational multi-alternativeness is evaluated on the basis of subjective entropy of preferences demonstrated by aircraft operators and aviation experts. When applying the maximum principle of subjective entropy, the optimal distributions of the preferences are obtained. The proposed concept allows finding the optimal distribution of the aircraft fleet according to the available maintenance alternatives. To optimize the above mentioned distribution, one may take into account the possible development and improvement of maintenance organizations and so called “shadow” components. The paper also discusses a significant approach that helps to evaluate the effectiveness of organizations functioning in the area of aviation. This evaluation can be carried out at both global and continental levels as well as state, operator, and airline levels. The respective modeling has been performed and is illustrated with diagrams.

On state pseudo-hoops

Recently, the bounded pseudo-hoops with internal states have been defined and studied. Some of results are based on the hypothesis that a bounded pseudo-hoop has the Glivenko and (mN) properties. In this paper we show that this hypothesis is superfluous, namely every good pseudo-hoop satisfies the Glivenko and (mN) properties and those results are reformulated without that hypothesis. The pointed pseudo-hoops are introduced and studied and the notion of state operator has been generalized for the case of unbounded pseudo-hoops. We define the Bosbach and Riečan states on pointed pseudo-hoops and we make some considerations regarding the relationship between the state operators and states on these structures.