On quantum corrections in higher-spin theory in flat space

We consider an interacting theory of an infinite tower of massless higher-spin fields in flat space with cubic vertices and their coupling constants found previously by Metsaev. We compute the one-loop bubble diagram part of the self-energy of the spin 0 member of the tower by summing up all higher-spin loop contributions. We find that the result contains an exponentially UV divergent part and we discuss how it could be cancelled by a tadpole contribution depending on yet to be determined quartic interaction vertex. We also compute the tree-level four-scalar scattering amplitude due to all higher-spin exchanges and discuss its inconsistency with the BCFW constructibility condition. We comment on possible relation to similar computations in AdS background in connection with AdS/CFT.Comment: 34 pages, minor corrections and references adde

On one loop corrections in higher spin gravity

We propose an approach to compute one-loop corrections to the four-point amplitude in the higher spin gravities that are holographically dual to free $O(N)$, $U(N)$ and $USp(N)$ vector models. We compute the double-particle cut of one-loop diagrams by expressing them in terms of tree level four-point amplitudes. We then discuss how the remaining contributions to the complete one-loop diagram can be computed. With certain assumptions we find nontrivial evidence for the shift in the identification of the bulk coupling constant and $1/N$ in accordance with the previously established result for the vacuum energy.Comment: 25 pages, several figures; few comments added, the discussion of the incompleteness of Vasiliev equations reduced; replaced with the published versio

Generalised model of wear in contact problems: the case of oscillatory load

In this short paper, we consider a sliding punch problem under recently proposed model of wear which is based on the Riemann-Liouville fractional integral relation between pressure and worn volume, and incorporates another additional effect pertinent to relaxation. A particular case of oscillatory (time-harmonic) load is studied. The time-dependent stationary state is identified in terms of eigenfunctions of an auxiliary integral operator. Convergence to this stationary state is quantified. Moreover, numerical simulations have been conducted in order to illustrate the obtained results and study qualitative dependence on two main model parameters

Magnetisation moment of a bounded 3D sample: asymptotic recovery from planar measurements on a large disk using Fourier analysis

We consider the problem of reconstruction of the overall magnetisation vector (net moment) of a sample from partial data of the magnetic field. Namely, motivated by a concrete experimental set-up, we deal with a situation when the magnetic field is measured on a portion of the plane in vicinity of the sample and only one (normal to the plane) component of the field is available. We assume the measurement area to be a sufficiently large disk (lying in a horizontal plane above the sample) and we obtain a set of estimates for the components of the net moment vector with the accuracy asymptotically improving with the increase of the radius of the measurement disk. Compared to our previous preliminary results, the asymptotic estimates are now rigorously justified and higher-order estimates are given. The presented approach also elucidates the derivation of asymptotic estimates of an arbitrary order. The obtained results are illustrated numerically and their robustness with respect to noise is discussed

Constrained optimization in classes of analytic functions with prescribed pointwise values

We consider an overdetermined problem for Laplace equation on a disk with partial boundary data where additional pointwise data inside the disk have to be taken into account. After reformulation, this ill-posed problem reduces to a bounded extremal problem of best norm-constrained approximation of partial L2 boundary data by traces of holomorphic functions which satisfy given pointwise interpolation conditions. The problem of best norm-constrained approximation of a given L2 function on a subset of the circle by the trace of a H2 function has been considered in [Baratchart \& Leblond, 1998]. In the present work, we extend such a formulation to the case where the additional interpolation conditions are imposed. We also obtain some new results that can be applied to the original problem: we carry out stability analysis and propose a novel method of evaluation of the approximation and blow-up rates of the solution in terms of a Lagrange parameter leading to a highly-efficient computational algorithm for solving the problem