Separation of variables in AdS/CFT: functional approach for the fishnet CFT

The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

Physical origin of glass formation from multicomponent systems

The origin of glass formation is one of the most fundamental issues in glass science. The glass-forming ability (GFA) of multicomponent systems, such as metallic glasses and phase-change materials, can be enormously changed by slight modifications of the constituted elements and compositions. However, its physical origin remains mostly unknown. Here, by molecular dynamics simulations, we study three model metallic systems with distinct GFA. We find that they have a similar driving force of crystallization, but a different liquid-crystal interface tension, indicating that the latter dominates the GFA. Furthermore, we show that the interface tension is determined by nontrivial coupling between structural and compositional orderings and affects crystal growth. These facts indicate that the classical theories of crystallization need critical modifications by considering local ordering effects. Our findings provide fresh insight into the physical control of GFA of metallic alloys and the switching speed of phase-change materials without relying on experience.

Chemo-Hydrodynamic Patterns and Instabilities

By modifying a physical property of a solution like its density or viscosity, chemical reactions can modify and even trigger convective flows. These flows in turn affect the spatiotemporal distribution of the chemical species. A nontrivial coupling between reactions and flows then occurs. We present simple model systems of this chemo-hydrodynamic coupling. In particular, we illustrate the possibility of chemical reactions controlling or triggering viscous fingering, Rayleigh–Taylor, double-diffusive, and convective dissolution instabilities. We discuss laboratory experiments performed to study these phenomena and compare the experimental results to theoretical predictions. In each case we contrast the chemo-hydrodynamic patterns and instabilities with those that develop in nonreactive systems and unify the different dynamics in terms of the common features of the related spatial mobility profiles.

No Small Hairs in Anisotropic Power-law Gauss-Bonnet Inflation

We will examine whether anisotropic hairs exist in a string-inspired scalar-Gauss-Bonnet gravity model with the absence of potential of scalar field during the inflationary phase. As a result, we are able to obtain the Bianchi type I power-law solution to this model under the assumption that the scalar field acts as the phantom field, whose kinetic is negative definite. However, the obtained anisotropic hair of this model turns out to be large, which is inconsistent with the observational data. We will therefore introduce a nontrivial coupling between scalar and vector fields such as \(f^2(\phi)F_{\mu\nu}F^{\mu\nu}\) into the scalar-Gauss-Bonnet model with the expectation that the anisotropic hair would be reduced to a small one. Unfortunately, the magnitude of the obtained anisotropic hair is still large. These results indicate that the scalar-Gauss-Bonnet gravity model with the absence of potential of scalar field might not be suitable to generate small anisotropic hairs during the inflationary phase.

Shaping membrane vesicles by adsorption of a semiflexible polymer

The adsorption of polymers onto fluid membranes is a problem of fundamental interest in biology and soft materials, in part because the flexibility of membranes can lead to nontrivial coupling between polymer and membrane configurations.

Black holes with regular horizons in Maxwell-scalar gravity

A class of exact static spherically symmetric solutions of the Einstein–Maxwell gravity coupled to a massless scalar field is obtained in the harmonic coordinates of Minkowski space-time. For each value of the coupling constant a, these solutions are characterized by a set of three parameters, the physical mass μ0, the electric charge Q0 and the scalar-field parameter k. We find that the solutions for both gravitational and electromagnetic fields are not only affected by the scalar field, but also the nontrivial coupling with matter constrains the scalar field itself. In particular, we find that the constant k differs generically from ±1/2, falling into the interval [Formula: see text]. It takes these values only for black holes or in the case when a scalar field [Formula: see text] is totally decoupled from the matter. Our results differ from those previously obtained in that the presence of an arbitrary coupling constant a gives an opportunity to rule out the nonphysical horizons. In one of the special cases, the obtained solution corresponds to a charged dilatonic black hole with only one horizon μ+ and hence to the Kaluza–Klein case. The most remarkable property of this result is that the metric, the scalar curvature, and both the electromagnetic and scalar fields are all regular on this surface. Moreover, while studying the dilaton charge, we found that the inclusion of the scalar field in the theory resulted in a contraction of the horizon. The behavior of the scalar curvature was analysed.

POST-INFLATIONARY COSMOLOGICAL MODEL BASED ON THE SEVEN-DIMENSIONAL SUPERGRAVITY

We study classical solutions of the bosonic sector of seven-dimensional supergravity theory. This study is three-fold: first, we look for power law solutions in a space which is the Cartesian product of a four-dimensional Robertson-Walker metric and a compact internal space; next, for the same geometric configuration, we sketch the phase diagram of all possible stable solutions; finally, we consider the evolution of scalar fluctuations on the background of the exact solutions found here. We observe that in spite of the presence of a potential term and a nontrivial coupling of three scalar fields, no inflationary scenario can emerge from such theory, and that all stable solutions display a big-bang type singularity. We conclude that the supersymmetric theories are well suited to describe the post-inflationary behavior of the Universe emerging from the inflationary phase before it enters the pure radiation stage.