A note on the SYK model with complex fermions

We consider a version of the Sachdev-Ye-Kitaev model with complex fermions. We apply the shadow formalism to find four-point functions in the leading order in $1/N$ and dimensions of operators present in the theory. We also compute the retarded kernel and show that the Lyapunov exponent for the mode corresponding to the $U(1)$ charge is zero.Comment: 32 page

N=2\mathcal N=2 SYK model in the superspace formalism

We use superspace methods to study an SYK-like model with $\mathcal N=2$ supersymmetry in one dimension, and an analog of this model in two dimensions. We find the four-point function as an expansion in the basis of eigenfunctions of the Casimir of $su(1,1|1)$. We also find retarded kernels and Lyapunov exponents for both cases.Comment: 42 page

BPS states in the Omega-background and torus knots

We clarify some issues concerning the central charges saturated by the extended objects in the SUSY $U(1)$ $4d$ gauge theory in the $\Omega$-background. The configuration involving the monopole localized at the domain wall is considered in some details. At the rational ratio $\frac{\epsilon_1}{\epsilon_2}=\frac{p}{q}$ the trajectory of the monopole provides the torus $(p,q)$ knot in the squashed three-sphere. Using the relation between the integrable systems of Calogero type at the rational couplings and the torus knots we interpret this configuration in terms of the auxiliary $2d$ quiver theory or $3d$ theory with nontrivial boundary conditions. This realization can be considered as the AGT-like representation of the torus knot invariants.Comment: 39 pages, 6 figure

RG limit cycles

In this review we consider the concept of limit cycles in the renormalization group flows. The examples of this phenomena in the quantum mechanics and field theory will be presented.Comment: 35 pages, 3 figures; Contribution to the "Pomeranchuk-100" Volum

L’image de la Russie ancienne dans l’opéra russe du xixe siècle

L’article s’intéresse à la représentation de la Russie ancienne dans l’opéra russe du classicisme au symbolisme. Tout au long du xixe siècle, la préférence est allée aux sujets empruntés aux contes et légendes (bylines). Dans les opéras de la période préromantique s’est constituée une image stable de la Rus´, fondée davantage sur la mythologie païenne et les poèmes épiques que sur les faits historiques. Les motifs liés au baptême de la Rus´ en 988 étaient bien moins répandus. À l’époque romantique, la Russie ancienne et sa représentation alimentent une sorte de compétition entre Mixail Glinka (Moscou) et Aleksej Verstovskij (Saint-Pétersbourg). Dans la seconde moitié du xixe siècle, l’image merveilleuse et traditionnelle de la Russie ancienne est reprise de façon neuve dans plusieurs opéras de Rimskij-Korsakov. Avec le Prince Igor d’après le Dit de l’ost d’Igor, Borodin rompt avec un certain nombre de stéréotypes.The article considers the evolution of the interpretations of Ancient Russian themes in operas from Classicism to Symbolism. During the whole century stories derived from tales and bylinas were most popular. The image of Ancient Russia based more on pagan mythology and heroic epic than on historical facts was already settled in pre-romantic ‘fairy’ operas. Plots connected with the Christening of Russia in 988 were much less widespread. It is in the field of Ancient Russian plots that St Petersburg composer Mixail Glinka and Muscovite Aleksej Verstovskij became rivals in the age of Romanticism. At the end of the19th century, the traditional fairytale image of Russia was radically developed in several operas by Nikolaj Rimskij-Korsakov while Alexander Borodin, in Prince Igor based on Slovo o polku Igoreve, definitely broke with the tradition of the stereotypes of Ancient Russia

Fluorescence Analysis of E. coli Bacteria in Water

The fluorescence analysis of Escherichia coli (E. coli) bacteria was done. It has been established that a luminescent signal from the one of metabolites (reduction form of nicotinamide adenine dinucleotide, NADH) can be adopted as a vitality indicator of the bacteria. This signal was chosen as an analytical signal. It was determined that the nature of this signal is fluorescence. In order to eliminate influence of the light scattering on this fluorescence signal optimal conditions were chosen

The Current State of the Telecommunications Market of the Republic of Mordovia

The article deals with the current state of the market of telecommunication services of the Republic of Mordovia, reveals the factors characterizing the market situation. On the example of the Republic of Mordovia the problem of telecommunication services market and priority directions of development are analyzed. The author substantiates the effectiveness of interaction of market factors and internal environment factors. The directions of further expansion of the market are offered and the General “risk zones” of the market of telecommunication services are investigated. The structure of the Russian telecommunications market and modern information and communication infrastructure in the Republic of Mordovia are analyzed