arXiv subjects

Dmitry Ponomarev

Publications and source records attributed to Dmitry Ponomarev.

At least 37 records · Page 2Linked to original sources

arXiv2022

On the exponential time-decay for the one-dimensional wave equation with variable coefficients

We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges for large times. We give explicit estimates of the rate of this exponential decay by two different techniques. The first one is based on the definition of a modified, weighted local energy, with suitably constructed weights. The second one is based on the integral formulation of the problem and, under a more restrictive assumption on the variation of the coefficients, allows us to obtain improved decay rates.

math.AP↗

arXiv2022

A short note on the appearance of the simplest antilinear ODE in several physical contexts

In this short note, we review several one-dimensional problems such as those involving linear Schroedinger equation, variable-coefficient Helmholtz equation, Zakharov-Shabat system and Kubelka-Munk equations. We show that they all can be reduced to solving one simple antilinear ordinary differential equation $u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}$ or its nonhomogeneous version $u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}+g\left(x\right)$, $x\in\left(0,x_{0}\right)\subset\mathbb{R}$. We point out some of the advantages of the proposed reformulation and call for further investigation of the obtained ODE.

math-ph↗

arXiv2022

An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $ω$, but is especially efficient for high-frequency problems. It is based on a time-domain approach and consists of three steps: \emph{i)} computation of a suitable incoming plane wavelet with compact support in the propagation direction; \emph{ii)} solving a scattering problem in the time domain for the incoming plane wavelet; \emph{iii)} reconstruction of the time-harmonic solution from the time-domain solution via a Fourier transform in time. An essential ingredient of the new method is a front-tracking mesh adaptation algorithm for solving the problem in \emph{ii)}. By exploiting the limited support of the wave front, this allows us to make the number of the required degrees of freedom to reach a given accuracy significantly less dependent on the frequency $ω$. We also present a new algorithm for computing the Fourier transform in \emph{iii)} that exploits the reduced number of degrees of freedom corresponding to the adapted meshes. Numerical examples demonstrate the advantages of the proposed method and the fact that the method can also be applied with external source terms such as point sources and sound-soft scatterers. The gained efficiency, however, is limited in the presence of trapping modes.

math.NA↗

arXiv2021

3d conformal fields with manifest $sl(2,\mathbb{C})$

In the present paper we construct all short representation of $so(3,2)$ with the $sl(2,\mathbb{C})$ symmetry made manifest due to the use of $sl(2,\mathbb{C})$ spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS${}_4$ suggested earlier. We then study unitarity of the resulting representations, identify them as the lowest-weight modules and as conformal fields in the three-dimensional Minkowski space. Finally, we compare these results with the existing literature and discuss the properties of these representations under contraction of $so(3,2)$ to the Poincare algebra.

hep-th↗

arXiv2021

Asymptotic solution to convolution integral equations on large and small intervals

We consider convolution integral equations on a finite interval with a real-valued kernel of even parity, a problem equivalent to finding a Wiener-Hopf factorisation of a notoriously difficult class of $2\times 2$ matrices. The kernel function is assumed to be sufficiently smooth and decaying for large values of the argument. Without loss of generality, we focus on a homogeneous equation and we propose methods to construct explicit asymptotic solutions when the interval size is large and small. The large interval method is based on a reduction of the original equation to an integro-differential equation on a half-line that can be asymptotically solved in a closed form. This provides an alternative to other asymptotic techniques that rely on fast (typically exponential) decay of the kernel function at infinity which is not assumed here. We also consider the problem on a small interval and show that finding its asymptotic solution can be reduced to solving an ODE. In particular, approximate solutions could be constructed in terms of readily available special functions (prolate spheroidal harmonics). Numerical illustrations of the obtained results are provided and further extensions of both methods are discussed.

math.SP↗

arXiv2020

Spinor-Helicity Formalism for Massless Fields in AdS$_4$ III: Contact Four-Point Amplitudes

We study contact four-point amplitudes in the spinor-helicity formalism in anti-de Sitter space. We find that these amplitudes can be brought to an especially simple form, which we call canonical. Next, we classify consistent contact amplitudes by requiring correct transformation properties with respect to the AdS isometry algebra. Finally, we establish a connection between the canonical form of AdS amplitudes and scalar multi-trace conformal primaries in flat space.

hep-th↗

arXiv2020

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.

hep-th↗

arXiv2020

From bulk loops to boundary large-N expansion

We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions. We show that, as in flat space, amplitude's singularities are associated with non-trivial cuts of the diagram and factorize into products of the coefficient functions for the subdiagrams resulting from these cuts. We consider an example of a one-loop four-point diagram in detail and then briefly discuss how the procedure can be extended to more general diagrams. Finally, we show that this analysis reproduces simple relations that follow from the large-N considerations on the boundary.

hep-th↗

arXiv2019

Spinor-Helicity Formalism for Massless Fields in AdS$_4$ II: Potentials

In a recent letter we suggested a natural generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.

hep-th↗

arXiv2019

Spinor-Helicity Formalism for Massless Fields in AdS${}_4$

In this letter we suggest a natural spinor-helicity formalism for massless fields in AdS${}_4$. It is based on the standard realization of the AdS${}_4$ isometry algebra $so(3,2)$ in terms of differential operators acting on $sl(2,\mathbb{C})$ spinor variables. We start by deriving the AdS counterpart of plane waves in flat space and then use them to evaluate simple scattering amplitudes. Finally, based on symmetry arguments we classify all three-point amplitudes involving massless spinning fields. As in flat space, we find that the spinor-helicity formalism allows to construct additional consistent interactions compared to approaches employing Lorentz tensors.

hep-th↗

arXiv2018

SafeSpec: Banishing the Spectre of a Meltdown with Leakage-Free Speculation

Speculative execution which is used pervasively in modern CPUs can leave side effects in the processor caches and other structures even when the speculated instructions do not commit and their direct effect is not visible. The recent Meltdown and Spectre attacks have shown that this behavior can be exploited to expose privileged information to an unprivileged attacker. In particular, the attack forces the speculative execution of a code gadget that will carry out the illegal read, which eventually gets squashed, but which leaves a side-channel trail that can be used by the attacker to infer the value. Several attack variations are possible, allowing arbitrary exposure of the full kernel memory to an unprivileged attacker. In this paper, we introduce a new model (SafeSpec) for supporting speculation in a way that is immune to side-channel leakage necessary for attacks such as Meltdown and Spectre. In particular, SafeSpec stores side effects of speculation in a way that is not visible to the attacker while the instructions are speculative. The speculative state is then either committed to the main CPU structures if the branch commits, or squashed if it does not, making all direct side effects of speculative code invisible. The solution must also address the possibility of a covert channel from speculative instructions to committed instructions before these instructions are committed. We show that SafeSpec prevents all three variants of Spectre and Meltdown, as well as new variants that we introduce. We also develop a cycle accurate model of modified design of an x86-64 processor and show that the performance impact is negligible. We build prototypes of the hardware support in a hardware description language to show that the additional overhead is small. We believe that SafeSpec completely closes this class of attacks, and that it is practical to implement.

cs.CR↗

arXiv2018

Chiral Higher Spin Theories and Self-Duality

We study recently proposed chiral higher spin theories - cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that they are naturally associated with gauge algebras, which manifest themselves in several related ways. Firstly, the chiral higher spin equations of motion can be reformulated as the self-dual Yang-Mills equations with the associated gauge algebras instead of the usual colour gauge algebra. We also demonstrate that the chiral higher spin field equations, similarly to the self-dual Yang-Mills equations, feature an infinite algebra of hidden symmetries, which ensures their integrability. Secondly, we show that off-shell amplitudes in chiral higher spin theories satisfy the generalised BCJ relations with the usual colour structure constants replaced by the structure constants of higher spin gauge algebras. We also propose generalised double copy procedures featuring higher spin theory amplitudes. Finally, using the light-cone deformation procedure we prove that the structure of the Lagrangian that leads to all these properties is universal and follows from Lorentz invariance.

hep-th↗

arXiv2018

A Note on (Non)-Locality in Holographic Higher Spin Theories

It was argued recently that the holographic higher spin theory features non-local interactions. We further elaborate on these results using the Mellin representation. The main difficulty previously encountered on this way is that the Mellin amplitude for the free theory correlator is ill-defined. To resolve this problem, instead of literally applying the standard definition, we propose to define this amplitude by linearity using decompositions, where each term has the associated Mellin amplitude well-defined. Up to a sign, the resulting amplitude is equal to the Mellin amplitude for the singular part of the quartic vertex in the bulk theory and, hence, can be used to analyze bulk locality. From this analysis we find that the scalar quartic self-interaction vertex in the holographic higher spin theory has a singularity of a special form, which can be distinguished from generic bulk exchanges. We briefly discuss the physical interpretation of such singularities and their relation to the Noether procedure.

hep-th↗

arXiv2017

Light-Front Higher-Spin Theories in Flat Space

We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields - the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.

hep-th↗

arXiv2016

Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure

We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes built from the light-cone Hamiltonian in the standard way. Then we find a general solution of these Ward identities. The solution admits a compact representation when written in the spinor-helicity form and is given by an arbitrary function of spinor products, satisfying well-known homogeneity constraints. Thus, we show that the light-cone consistent deformation procedure inevitably leads to a certain off-shell version of the spinor-helicity approach. We discuss how the relation between the two approaches can be employed to facilitate the search of consistent interaction of massless higher-spin fields.

hep-th↗

arXiv2016

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.

hep-th↗

arXiv2016

Bulk quartic vertices from boundary four-point correlators

We present arguments which suggest that the bulk higher-spin gravity duals of weakly-coupled conformal field theories obey some refined notion of locality. In particular, we discuss the Mellin amplitude programme in this context. We focus on the $O(N)$ vector model and minimal higher-spin gravity as a paradigmatic example of such holographic dual pairs. We restrict ourselves to three- and four-point functions of scalar primary operators, but the qualitative conclusions are expected to hold for the generic case.

hep-th↗

arXiv2016

New Unfolded Higher Spin Systems in $AdS_3$

We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in $AdS_3$ containing a parity breaking mass parameter. They include deformations of the linearisations of the Prokushkin--Vasiliev higher spin theory around its critical points. They also provide unfolded formulations of linearized topologically massive higher spin fields including their critical versions. The gauge invariant degrees of freedom are captured by infinite towers of zero forms. We also introduce two inequivalent sets of gauge potentials given by trace constrained Fronsdal fields and trace unconstrained metric-like fields.

hep-th↗