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Oleg Evnin

Publications and source records attributed to Oleg Evnin.

At least 73 records · Page 4Linked to original sources
arXiv2016

Detailed ultraviolet asymptotics for AdS scalar field perturbations

We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.

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arXiv2016

AdS perturbations, isometries, selection rules and the Higgs oscillator

Dynamics of small-amplitude perturbations in the global anti-de Sitter (AdS) spacetime is restricted by selection rules that forbid effective energy transfer between certain sets of normal modes. The selection rules arise algebraically because some integrals of products of AdS mode functions vanish. Here, we reveal the relation of these selection rules to AdS isometries. The formulation we discover through this systematic approach is both simpler and stronger than what has been reported previously. In addition to the selection rule considerations, we develop a number of useful representations for the global AdS mode functions, with connections to algebraic structures of the Higgs oscillator, a superintegrable system describing a particle on a sphere in an inverse cosine-squared potential, where the AdS isometries play the role of a spectrum-generating algebra.

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arXiv2015

Ultraviolet asymptotics and singular dynamics of AdS perturbations

Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order 1/epsilon^2. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive relations for the coefficients of the time-averaged theory that are likely to be useful for evaluating them more efficiently in numerical simulations.

gr-qc↗
arXiv2015

Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.

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arXiv2015

A Hidden Symmetry of AdS Resonances

Recent investigations have revealed powerful selection rules for resonant energy transfer between modes of non-linear perturbations in global anti-de Sitter (AdS) space-time. It is likely that these selection rules are due to the highly symmetric nature of the underlying AdS background, though the precise relation has remained unclear. In this article, we demonstrate that the equation satisfied by the scalar field mode functions in AdS(d+1) has a hidden SU(d) symmetry, and explicitly specify the multiplets of this SU(d) symmetry furnished by the mode functions. We also comment on the role this structure might play in explaining the selection rules.

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arXiv2015

Renormalization, averaging, conservation laws and AdS (in)stability

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

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arXiv2014

Renormalization group, secular term resummation and AdS (in)stability

We revisit the issues of non-linear AdS stability, its relation to growing (secular) terms in naive perturbation theory around the AdS background, and the need and possible strategies for resumming such terms. To this end, we review a powerful and elegant resummation method, which is mathematically identical to the standard renormalization group treatment of ultraviolet divergences in perturbative quantum field theory. We apply this method to non-linear gravitational perturbation theory in the AdS background at first non-trivial order and display the detailed structure of the emerging renormalization flow equations. We prove, in particular, that a majority of secular terms (and the corresponding terms in the renormalization flow equations) that could be present on general grounds given the spectrum of frequencies of linear AdS perturbations, do not in fact arise.

gr-qc↗
arXiv2013

Strings in compact cosmological spaces

We confront the problem of giving a fundamental definition to perturbative string theory in spacetimes with totally compact space (taken to be a torus for simplicity, though the nature of the problem is very general) and non-compact time. Due to backreaction induced by the presence of even a single string quantum, the usual formulation of perturbative string theory in a fixed classical background is infrared-divergent at all subleading orders in the string coupling, and needs to be amended. The problem can be seen as a closed string analogue of D0-brane recoil under an impact by closed strings (a situation displaying extremely similar infrared divergences). Inspired by the collective coordinate treatment of the D0-brane recoil, whereby the translational modes of the D0-brane are introduced as explicit dynamical variables in the path integral, we construct a similar formalism for the case of string-induced gravitational backreaction, in which the spatially uniform modes of the background fields on the compact space are quantized explicitly. The formalism can equally well be seen as an ultraviolet completion of a minisuperspace quantum cosmology with string degrees of freedom. We consider the amplitudes for the universe to have two cross-sections with specified spatial properties and string contents, and show (at the first non-trivial order) that they are finite within our formalism.

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arXiv2013

Microscopic approach to string gas cosmology

In this contribution to the proceedings of the Conference on Modern Physics of Compact Stars and Relativistic Gravity in Yerevan, Armenia (September 18-21, 2013), I review recent work attempting to give a fundamental definition to string evolution in a dynamical, fully compact universe, and present a sketch of how the resulting formalism can be used for addressing questions of phenomenological significance in the field of string gas cosmology.

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arXiv2012

Quantum backreaction in string theory

There are situations in string theory when a finite number of string quanta induce a significant backreaction upon the background and render the perturbation theory infrared-divergent. The simplest example is D0-brane recoil under an impact by closed strings. A more physically interesting case is backreaction on the evolution of a totally compact universe due to closed string gas. Such situations necessitate qualitative amendments to the traditional formulation of string theory in a fixed classical background. In this contribution to the proceedings of the XVII European Workshop on String Theory in Padua, I review solved problems and current investigations in relation to this kind of quantum backreaction effects.

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arXiv2011

Randomized Wilson loops, reduced models and the large D expansion

Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. These integrals are known to simplify further when the number of matrices D (corresponding to the number of space-time dimensions in the gauge theory) becomes large. Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi-Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.

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arXiv2011

Intersecting black branes in strong gravitational waves

We consider intersecting black branes with strong gravitational waves propagating along their worldvolume in the context of supergravity theories. Both near-horizon and space-filling gravitational wave modes are included in our ansatz. The equations of motion (originally, partial differential equations) are shown to reduce to ordinary differential equations, which include a Toda-like system. For special arrangements of intersecting black branes, the Toda-like system becomes integrable, permitting a more thorough analysis of the gravitational equations of motion.

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arXiv2011

Light-like Big Bang singularities in string and matrix theories

Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like Big Bang models, presenting both solved and open problems.

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arXiv2011

Extended black holes in strong gravitational waves

We describe a large class of solutions in pure gravity, dilaton gravity and supergravity corresponding to extended higher-dimensional black holes with strong (non-linear) gravitational waves propagating along their worldvolume. For pure gravity, the extended black holes are higher-dimensional analogs of the point-like Schwarzschild black hole in four dimensions. For supergravity, they are non-extremal p-branes. The gravitational waves can be both space-filling and localized around the worldvolume of the extended black holes. The solutions we present contain a large number of arbitrary functions of the light-cone time describing the amplitudes of different non-linear gravitational wave modes.

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arXiv2011

Adiabaticity and emergence of classical space-time in time-dependent matrix theories

We discuss the low-curvature regime of time-dependent matrix theories proposed to describe non-perturbative quantum gravity in asymptotically plane-wave space-times. The emergence of near-classical space-time in this limit turns out to be closely linked to the adiabaticity of the matrix theory evolution. Supersymmetry restoration at low curvatures, which is crucial for the usual space-time interpretation of matrix theories, becomes an obvious feature of the adiabatic regime.

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arXiv2009

p-branes on the waves

We present a large family of simple, explicit ten-dimensional supergravity solutions describing extended extremal supersymmetric Ramond-Ramond p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. Generalizations to the non-extremal case are not analyzed explicitly, but can be pursued as indicated.

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arXiv2009

Can free strings propagate across plane wave singularities?

We study free string propagation in families of plane wave geometries developing strong scale-invariant singularities in certain limits. We relate the singular limit of the evolution for all excited string modes to that of the center-of-mass motion (the latter existing for discrete values of the overall plane wave profile normalization). Requiring that the entire excitation energy of the string should be finite turns out to be quite restrictive and essentially excludes consistent propagation across the singularity, unless dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).

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