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Conformal higher-spin gravity is the log-divergent part of the effective action of the scalar field coupled to background fields via higher-spin currents, as was defined by Segal and Tseytlin, which can be worked out over the flat space background. We revisit the problem of the scalar field in a higher-spin background and propose a manifestly covariant version thereof. The construction utilizes the Fedosov quantization of the cotangent bundle and the action is written with the help of the trace on a curved phase space that is provided by the Feigin--Felder--Shoikhet cocycle. The same construction allows one to formulate quantum mechanics on a curved space, the phase space being the cotangent bundle.

We address the issue of electromagnetic interaction for massive higher-spin fields in $3d$ Minkowski space. We show that consistent field equations can be obtained through the dimensional reduction of the higher-spin extension of self-dual Yang-Mills theory, which itself is a truncation of chiral higher-spin gravity in four dimensions. The resulting electromagnetic field satisfies the Bogomolny equation, and the interaction is non-minimal with the gyromagnetic ratio given by $g=1/s$, where $s$ is the spin. As a by-product, we obtain a new Lagrangian for free massive higher-spin fields in $3d$., Comment: 24 pages

We study how the supercurrent flow pattern is altered by inhomogeneities in superconducting films. Working in the vicinity of the critical temperature and assuming a model of short-range disorder in the quadratic term of the Ginzburg-Landau functional, we develop a perturbation theory in the inhomogeneity strength. Absorbing the ultraviolet divergences into the renormalization of the critical temperature, we arrive at a well-defined theory governed by large-scale physics. In the presence of inhomogeneities, the correlation functions of the order parameter and supercurrent exhibit a long-range power-law behavior, which can be attributed to the mixing of the amplitude and phase modes. The fluctuation magnitude grows with increasing the average current, and the system becomes strongly inhomogeneous near the critical current., Comment: 14 pages, 6 figures

This paper investigates the application of game-theoretic principles combined with advanced Kalman filtering techniques to enhance maritime target tracking systems. Specifically, the paper presents a two-player, imperfect information, non-cooperative, sequential game framework for optimal decision making for a tracker and an evader. The paper also investigates the effectiveness of this game-theoretic decision making framework by comparing it with single-objective optimisation methods based on minimising tracking uncertainty. Rather than modelling a zero-sum game between the tracker and the evader, which presupposes the availability of perfect information, in this paper we model both the tracker and the evader as playing separate zero-sum games at each time step with an internal (and imperfect) model of the other player. The study defines multi-faceted winning criteria for both tracker and evader, and computes winning percentages for both by simulating their interaction for a range of speed ratios. The results indicate that game theoretic decision making improves the win percentage of the tracker compared to traditional covariance minimization procedures in all cases, regardless of the speed ratios and the actions of the evader. In the case of the evader, we find that a simpler linear escape action is most effective for the evader in most scenarios. Overall, the results indicate that the presented sequential-game based decision making framework significantly improves win percentages for a player in scenarios where that player does not have inherent advantages in terms of starting position, speed ratio, or available time (to track / escape), highlighting that game theoretic decision making is particularly useful in scenarios where winning by using more traditional decision making procedures is highly unlikely.

Massless higher-spin fields show no preference for any value of the cosmological constant in $3d$. All matter-free higher-spin gravities in 3d are equivalent to Chern-Simons theories with an appropriate choice of gauge algebra. For various reasons, including holography, it is important to enrich them with matter fields. In $(A)dS_3$, the coupling of matter fields to higher-spin fields is well-known to the leading order and is determined by the representation theory. We extend this result to flat space, where the relevant higher-spin algebra is the Poisson algebra, aka $w_{1+\infty}$. However, we show that both in flat and $(A)dS_3$ spaces there are no nontrivial higher order deformations/interactions. Nevertheless, by enlarging the field content with some auxiliary fields and taking advantage of the chiral higher-spin gravity's vertices, it is possible to construct an exotic matter-coupled theory on $(A)dS_3$. It also admits a flat limit. The equations of motion have the form of a Poisson sigma-model and a meaningful action has the form of a Courant sigma-model. We also explore the potential for embedding this theory into a holographic duality., Comment: 43 pages

Massive higher-spin fields are difficult to introduce consistent interactions, including electromagnetic and gravitational ones which are clearly exhibited by (non-elementary) higher-spin particles in nature. We construct an action that describes consistent interactions of massive spin three-half field with a constant electromagnetic background. We also work out the relation to the chiral approach., Comment: 25 pages

Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance., Comment: typos fixed, few comments added, published version, 31 pages

Chiral higher-spin gravity is a higher-spin extension of both self-dual Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in four dimensions. Its existence implies that there are two closed subsectors in Chern-Simons matter theories. We make first steps in identifying these (anti-)chiral subsectors directly on the CFT side, which should result in a holographically dual pair where both sides are nontrivial, complete, yet exactly soluble. We also discuss closely related theories: self-dual Yang-Mills (SDYM) and self-dual gravity (SDGR) in the holographic context., Comment: 27 pages+17 pages appendices, 1 figure

Higher spin gravities do not have a low energy limit where higher-spin fields decouple from gravity. Nevertheless, it is possible to construct fine-tuned exact solutions that activate low-spin fields without sourcing the higher-spin fields. We show that BPST (Belavin-Polyakov-Schwartz-Tyupkin) instanton is an exact solution of Chiral Higher Spin Gravity, i.e. it is also a solution of the holographic dual of Chern-Simons matter theories. This gives an example of a low-spin solution. The instanton sources the opposite helicity spin-one field and a scalar field. We derive an Effective Field Theory that describes the coupling between an instanton and the other two fields, whose action starts with the Chalmers-Siegel action and has certain higher derivative couplings., Comment: 34 pages, published version

Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the $A_\infty$-relations via Stokes' theorem by constructing a closed form and a configuration space whose boundary components lead to the $A_\infty$-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems., Comment: many figures, too many pages, published version

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin s=0,1/2,1,...,$\infty$, from which we extract the corresponding classical amplitude to all orders in the spin vector $S^\mu$. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-s Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin., Comment: 7 pages + refs; v3 minor improvements, journal version

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic amplitude of Arkani-Hamed--Huang--Huang. The same is achieved for the root-Kerr theory, i.e. for the minimal electromagnetic interaction of a massive higher-spin field., Comment: 23 pages

Motivated by the generation of action principles from off-shell dualisation, we present a general class of free, topological theories in three dimensional Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two case, we recover a dual reformulation of the triplet system already known, while the higher-spin systems that we obtain seem to be new. They are associated with wild quivers. We study in which situations these exotic (or strange) higher-spin models can be extended to dS${}_3$ and AdS${}_3$ backgrounds, revealing that the flat limit of such models, when they exist, admits a one-parameter freedom. Interactions are studied in the simplest higher-spin case featuring spin-2 and spin-3 fields. We then give several higher-spin generalisations of these strange systems., Comment: 53 pages

We develop massive higher-spin theory as a framework for describing dynamics of rotating compact objects, such as Kerr black holes. In this paper, we explore gauge interactions up to quartic order and corresponding Compton amplitudes of higher-spin massive objects coupled to electromagnetism and Yang-Mills theory. Their classical counterparts are known as root-Kerr gauge-theory solutions, whose amplitudes are closely related to those of Kerr black holes. We use three distinct approaches: (i) massive higher-spin gauge symmetry to introduce cubic interactions for all spins and the quartic interactions up to spin 3, which is implemented both off shell and via Ward identities; (ii) a chiral higher-spin approach to construct quartic Lagrangians with correct degrees of freedom to all spins; (iii) on-shell functional patterns before and after taking the classical limit to constrain the Compton amplitudes. As final results, we arrive at simple local formulae for the candidate root-Kerr Compton amplitudes both in the quantum regime and classical limit, to all orders in spin. This is a precursor to the gravitational Kerr case, which is presented in a follow-up paper., Comment: 65p + appx., 1 figure

The state-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb or Cs). Increasing frequency stability of the clocks is an urgent issue that will lead to significant progress in many fields of application. Here, we examine a light field configuration composed of two bichromatic light beams with opposite handedness of their circular polarization. The beams are in resonance with optical transitions in the Cs D$_1$ line ($\lambda$$\approx$$895$ nm). This configuration has already been known for observing CPT resonances of an increased contrast compared to a standard single-beam scheme. However, in contrast to previous studies, we use a scheme with two independent pump and probe beams, where the probe beam transmission is separately monitored. The experiments are carried out with a buffer-gas-filled $5$$\times$$5$$\times$$5$ mm$^3$ vapor cell. It is shown that the resonance's line shape acquires asymmetry which can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way how this asymmetry can help to significantly mitigate the influence of ac Stark (light) shift on a long-term frequency stability of CPT clocks. The experimental verification is performed both with a distributed-Bragg-reflector (DBR) laser and a vertical-cavity surface-emitting laser (VCSEL). The latter has a particular importance for developing MACs. The results of experiments are in qualitative agreement with analytical theory based on a double $\Lambda$ scheme of atomic energy levels., Comment: 13 pages, 10 figures, 67 references

It is proved that any function of a Lusin-type class, the class of $ACG_r$-functions, is differentiable almost everywhere in the sense of a derivative defined in the space~$L^r$, $1\le r<\infty$. This leads to obtaining a full descriptive characterization of a Henstock-Kurzweil-type integral, the $HK_r$-integral, which serves to recover functions from their $L^r$-derivatives. The class $ACG_r$ is compared with the classical Lusin class $ACG$ and it is shown that a continuous $ACG$-function can fail to be $L^r$-differentiable almost everywhere.

In this review, we describe several approximations in the theory of Laplacian transport near complex or heterogeneously reactive boundaries. This phenomenon, governed by the Laplace operator, is ubiquitous in fields as diverse as chemical physics, hydrodynamics, electrochemistry, heat transfer, wave propagation, self-organization, biophysics, and target search. We overview the mathematical basis and various applications of the effective medium approximation and the related boundary homogenization when a complex heterogeneous boundary is replaced by an effective much simpler boundary. We also discuss the constant-flux approximation, the Fick-Jacobs equation, and other mathematical tools for studying the statistics of first-passage times to a target. Numerous examples and illustrations are provided to highlight the advantages and limitations of these approaches.

We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string's spacetime Lorentz algebra commutes with a certain inductive limit of $sp(\bullet)$, with the Virasoro constraints forming a subalgebra of the Howe dual algebra $sp(\bullet)$. There are then infinitely many simple trajectories of states, which are lowest-weight representations of $sp(\bullet)$ and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes., Comment: 47 pages, a number of pictures; some typos fixed, replaced with the published version

We study the electron-phonon relaxation in the model of a granular metal film, where the grains are formed by regularly arranged potential barriers of arbitrary transparency. The relaxation rate of Debye acoustic phonons is calculated, taking into account two mechanisms of electron-phonon scattering: the standard Fr\"ohlich interaction of the lattice deformation with the electron density and the interaction mediated by the displacement of grain boundaries dragged by the lattice vibration. At the lowest temperatures, the electron-phonon cooling power follows the power-law temperature dependence typical for clean systems but with the prefactor growing as the transparency of the grain boundaries decreases., Comment: 9 pages, 5 figures (minor revision, role of inelastic processes discussed)

In this paper we consider the problem of estimation of scalar field distribution (e.g. pollutant, moisture, temperature) from noisy measurements collected by unmanned autonomous vehicles such as UAVs. The field is modelled as a sum of Fourier components/modes, where the number of modes retained and estimated determines in a natural way the approximation quality. An algorithm for estimating the modes using an online optimization approach is presented, under the assumption that the noisy measurements are quantized. The algorithm can also estimate time-varying fields through the introduction of a forgetting factor. Simulation studies demonstrate the effectiveness of the proposed approach., Comment: Add Section V-C

For a model of a 3D coating composed of a bi-periodic system of parallel riblets with gaps we analytically derive an approximate formula for the effective slip length (an offset from the flat surface at which the flow velocity would extrapolate to zero) as a function of the geometry of the system (riblet period, riblet height, and relative gap size). This formula is valid for an arbitrary fraction of gaps (i.e from narrow riblets to narrow gaps) and agrees with the known analytical results for the 2D periodic coating of riblets without gaps. We validate our analytical results with the numerical solution of the equations of the viscous (creeping) flow over the riblets with gaps.

Conformal Higher Spin Gravity is a higher spin extension of Weyl gravity and is a family of local higher spin theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between higher spin symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal higher spin fields (Fradkin-Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin-Felder-Shoikhet cocycle of Weyl algebra, which extends Segal's action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle., Comment: 37 pages, 1 figure; v2: typos corrected, appendix C modified and references added

We propose a new (chiral) description of partially-massless fields in $4d$, including the partially-massless graviton, that is similar to the pure connection formulation for gravity and massless higher spin fields, the latter having a clear twistor origin. The new approach allows us to construct complete examples of higher spin gravities with (partially-)massless fields that feature Yang--Mills and current interactions., Comment: 22 pages, 3 figures

We propose that the dynamics of Kerr black holes is strongly constrained by the principle of gauge symmetry. We initiate the construction of EFTs for Kerr black holes of any integer quantum spin s using Stueckelberg fields, and show that the known three-point Kerr amplitudes are uniquely predicted using massive higher-spin gauge symmetry. This symmetry is argued to be connected to an enhanced range of validity for the Kerr EFTs. We consider the closely related root-Kerr electromagnetic solution in parallel, for which the dynamical interactions with photons are also constrained by massive higher-spin gauge symmetry. Finally, the spin-s Compton amplitudes are analyzed, and we discuss contact-term constraints at s=2 from Ward identities., Comment: 6 pages, v2: published version

We calculate the quasiparticle density of states (DoS) inside the vortex core in a granular superconductor, generalizing the classical solution applicable for dirty superconductors. A discrete version of the Usadel equation for a vortex is derived and solved numerically for a broad range of parameters. Electron DoS is found to be gapful when the vortex size $\xi$ becomes comparable to the distance between neighboring grains $l$. Minigap magnitude $E_g$ grows from zero at $\xi \approx 1.4 l$ to third of superconducting gap $\Delta_0 $ at $\xi \approx 0.5 l$. The absence of low-energy excitations is the main ingredient needed to understand strong suppression of microwave dissipation recently observed in a mixed state of granular Al.

We investigate the survival probability of a particle diffusing between two parallel reflecting planes toward a periodic array of absorbing pillars. We approximate the periodic cell of this system by a cylindrical tube containing a single pillar. Using a mode matching method, we obtain an exact solution of the modified Helmholtz equation in this domain that determines the Laplace transform of the survival probability and the associated distribution of first-passage times. This solution reveals the respective roles of several geometric parameters: the height and radius of the pillar, the inter-pillar distance, and the distance between confining planes. This model allows us to explore different asymptotic regimes in the probability density of the first-passage time. In the practically relevant case of a large distance between confining planes, we argue that the mean first-passage time is much larger than the typical time and thus uninformative. We also illustrate the failure of the capacitance approximation for the principal eigenvalue of the Laplace operator. Some practical implications and future perspectives are discussed.

We locate Musial\,\&\,Sagher's concept of HK$_r$-inte\-gration within the approximate Henstock--Kurzweil integral theory. If to restrict HK$_r$-integral by requirement that the indefinite HK$_r$-integral is {\em continuous}, then it is included even in the classical Denjoy--Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.

Using the framework of supersymmetric non-linear $\sigma$-model we develop a general non-perturbative characterisation of universal features of the density $\rho(\Gamma)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $\rho(\Gamma)\sim \Gamma^{-1}$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim \Gamma^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $\rho(\Gamma)\sim \Gamma^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts., Comment: The previous letter-style version is replaced by a full-length article