Superconformal indices of N=4 dual field theories

Using the superconformal indices techniques, we construct new interesting conjectures for the elliptic hypergeometric integral identities based on the exceptional groups $G_2$ and $F_4$. These identities arise from $S$-dualities for $\mathcal{N}=4$ supersymmetric Yang-Mills theories with $G_2$ and $F_4$ gauge groups

The Phenomenon of Indirect Learning: Brain Mechanisms and Models

AbstractWe studied an artificially constructed isomorphism between denotative (color) and lexical (geometric shapes) spaces and revealed the dynamics of formation of color-semantic representations in the process of indirect learning. We have detected the component of evoked potential (EP), which describes its changes from trial to trial in the process of learning; it significantly correlates with the value and direction of the errors. The results confirm the role of the brain structures that control movement (globus pallidus, caudate nucleus) in problems reconfiguring the system of relations between the sensory attributes of the reception of sign (visual cortex), and attributes of denotatum stored in memory (frontal cortex and parahippocampal gyrus) that occur during the formation of concepts

Supersymmetric dualities beyond the conformal window

Using the superconformal (SC) indices techniques, we construct Seiberg type dualities for $\mathcal{N}=1$ supersymmetric field theories outside the conformal windows. These theories are physically distinguished by the presence of chiral superfields with small or negative $R$-charges.Comment: 4pp; v2: clarification of the results, accepted in Phys. Rev. Let

Производство, потребление и медиа: к постановке модели трехстороннего рынка

. A wide body of literature on economic theory is devoted to the analysis of industrial goods markets with the possibility of advertising influence on demand. However, these models do not view media as industry entities with their own strategic goals and objectives. On the other hand, the main models of behavior of media firms, considering them as platforms connecting consumers with manufacturers (models of two-sided markets), do not take into account the simultaneous consumption of the products of industrial firms and their content by the audience and the production nature of the problems solved by industrial firms. In this regard, this paper proposes a methodology for constructing models of a new type of market, including three types of participants - consumers, media firms and industrial manufacturing firms. In accordance with the proposed methodology, a model of the simplest three-sided market is constructed, for which the questions of existence and properties of equilibrium are discussed. The results of such modeling can find application in the study of intersectoral interaction between the media industry and any industry

Infrared Finite Observables in N=8 Supergravity

Using the algorithm of constructing the IR finite observables suggested and discussed in details in our previous publications, we consider construction of such observables in N=8 SUGRA in NLO of PT. In general, contrary to the amplitudes defined in the presence of some IR regulator, such observables do not reveal any simple structure