Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence

We consider \gamma-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real \gamma-deformations of the AdS_5xS^5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.Comment: 18 pages, no figure, LaTeX, v2:references and further clarifications adde

On the classical equivalence of monodromy matrices in squashed sigma model

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.Comment: 32pages, 3figures, references added, introduction and discussion sections revise

The classical origin of quantum affine algebra in squashed sigma models

We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.Comment: 25 pages, 2 figure

Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments it is found that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength, and is unaffected by Ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly-isothermal calculations, where pressure varies little with time. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of non-steady magnetic reconnection.Comment: 45 pages, 5 tables, 17 figures, accepted for publication in Ap

Hybrid classical integrable structure of squashed sigma models -- a short summary

We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1) the rational description and 2) the trigonometric description. It is possible to construct two different types of Lax pairs depending on the descriptions, and the classical integrability is shown by computing classical r/s-matrices satisfying the extended Yang-Baxter equation in both descriptions. In the former the system is described as an integrable system of rational type. On the other hand, in the latter it is described as trigonometric type. There exists a non-local map between the two descriptions and those are equivalent. This is a non-local generalization of the left-right duality in principal chiral models.Comment: 10 pages, Proceedings of QTS7, Prague, Czech Republic, 201

Signatures of r-process elements in kilonova spectra

Binary neutron star (NS) mergers have been expected to synthesize r-process elements and emit radioactively powered radiation, called kilonova. Although r-process nucleosynthesis was confirmed by the observations of GW170817/AT2017gfo, no trace of individual elements has been identified except for strontium. In this paper, we perform systematic calculations of line strength for bound-bound transitions and radiative transfer simulations in NS merger ejecta toward element identification in kilonova spectra. We find that Sr II triplet lines appear in the spectrum of a lanthanide-poor model, which is consistent with the absorption feature observed in GW170817/AT2017gfo. The synthetic spectrum also shows the strong Ca II triplet lines. This is natural because Ca and Sr are co-produced in the material with relatively high electron fraction and their ions have similar atomic structures with only one s-electron in the outermost shell. The line strength, however, highly depends on the abundance distribution and temperature in the ejecta. For our lanthanide-rich model, the spectra show the features of doubly ionized heavy elements, such as Ce, Tb and Th. Our results suggest that the line forming region of GW170817/AT2017gfo was lanthanide-poor. We show that the Sr II and Ca II lines can be used as a probe of physical conditions in NS merger ejecta. Absence of the Ca II line features in GW170817/AT2017gfo implies that the Ca/Sr ratio is = 0.40 and entropy per nucleon (in units of Boltzmann constant) >= 25

Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry

We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R due to the deformation. According to this symmetry, there are two descriptions to describe the classical dynamics of the system, 1) the SL(2,R)_L description and 2) the enhanced U(1)_R description. In the former 1), we show that the Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a Lax pair is constructed with the improved current and the classical integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we find a non-local current by using a scaling limit of warped AdS_3 and that it enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is presented and the corresponding r/s-matrices are also computed. The two descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde

Dynamical transitions and sliding friction in the two-dimensional Frenkel-Kontorova model

The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular dynamics. Dynamical phase transitions between pinned solid, sliding commensurate and incommensurate solids and hysteresis effects are found that are qualitatively similar to the results for a Lennard-Jones model, thus demonstrating the universal nature of these features.Comment: 11 pages, 12 figures, to appear in Phys. Rev.

Investigating slim disk solutions for HLX-1 in ESO 243-49

The hyper luminous X-ray source HLX-1 in the galaxy ESO 243-49, currently the best intermediate mass black hole candidate, displays spectral transitions similar to those observed in Galactic black hole binaries, but with a luminosity 100-1000 times higher. We investigated the X-ray properties of this unique source fitting multi-epoch data collected by Swift, XMM-Newton & Chandra with a disk model computing spectra for a wide range of sub- and super-Eddington accretion rates assuming a non-spinning black hole and a face-on disk (i = 0 deg). Under these assumptions we find that the black hole in HLX-1 is in the intermediate mass range (~2 x 10^4 M_odot) and the accretion flow is in the sub-Eddington regime. The disk radiation efficiency is eta = 0.11 +/-0.03. We also show that the source does follow the L_X ~ T^4 relation for our mass estimate. At the outburst peaks, the source radiates near the Eddington limit. The accretion rate then stays constant around 4 x 10^(-4) M_odot yr^(-1) for several days and then decreases exponentially. Such "plateaus" in the accretion rate could be evidence that enhanced mass transfer rate is the driving outburst mechanism in HLX-1. We also report on the new outburst observed in August 2011 by the Swift-X-ray Telescope. The time of this new outburst further strengthens the ~1 year recurrence timescale.Comment: 24 pages, 10 figures, accepted for publication in Ap