The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.Comment: 29 pages, 13 figure

The lowest modes around Gaussian solutions of tensor models and the general relativity

In the previous paper, the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-three tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R^2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.Comment: 31 pages, 8 figures, Added references, minor corrections, a misleading figure replace

Aeolian sans ripples: experimental study of saturated states

We report an experimental investigation of aeolian sand ripples, performed both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed, we can identify three regimes: appearance of an initial wavelength, coarsening of the pattern and finally saturation of the ripples. We show that both initial and final wavelengths, as well as the propagative speed of the ripples, are linear functions of the wind velocity. Investigating the evolution of an initially corrugated bed, we exhibit non-linear stable solutions for a finite range of wavelengths, which demonstrates the existence of a saturation in amplitude. These results contradict most of the models.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Title changed, figures corrected and simplified, more field data included, text clarifie

Superstring field theory equivalence: Ramond sector

We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.Comment: v1: 24 pages. v2: 27 pages, significant modifications of the presentation, new section, typos corrected, references adde

Energy from the gauge invariant observables

For a classical solution |Psi> in Witten's cubic string field theory, the gauge invariant observable is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to V, between the trivial vacuum and the one described by |Psi>. For a static solution |Psi>, if V is taken to be the graviton vertex operator with vanishing momentum, the gauge invariant observable is expected to be proportional to the energy of |Psi>. We prove this relation assuming that |Psi> satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.Comment: 27 pages; v5: minor revision in section 2, results unchange

Relevant Deformations in Open String Field Theory: a Simple Solution for Lumps

We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two--dimensional world-sheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.Comment: 45 pages. v2: typos and minor improvements. v3: submitted to jhe

Towards mirror symmetry \`a la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and \hat{M}. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3)xSU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.Comment: 30 pages, 3 figures, LaTeX; v2: references adde

Tachyon Vacuum in Cubic Superstring Field Theory

In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansion. Second, the solution {\it vanishes} in the GSO$(-)$ sector, implying a ``tachyon vacuum'' solution exists even for a {\it BPS} D-brane.Comment: 16 pages, 2 figure

The impact of the method of consent on response rates in the ISAAC time trends study.

BACKGROUND: Centres in Phases I and III of the International Study of Asthma and Allergies in Childhood (ISAAC) programme used the method of consent (passive or active) required by local ethics committees. METHODS: Retrospectively, relationships between achieved response rates and method of consent for 13-14 and 6-7-year-olds (adolescents and children, respectively), were examined between phases and between English and non-English language centres. RESULTS: Information was obtained for 113 of 115 centres for adolescents and 72/72 centres for children. Both age groups: most centres using passive consent achieved high response rates (>80% adolescents and >70% children). English language centres using active consent showed a larger decrease in response rate. Adolescents: seven centres changed from passive consent in Phase I to active consent in Phase III (median decrease of 13%), with five centres showing lower response rates (as low as 34%). Children: no centre changed consent method between phases. Centres using active consent had lower median response rates (lowest response rate 45%). CONCLUSION: The requirement for active consent for population school-based questionnaire studies can impact negatively on response rates, particularly English language centres, thus adversely affecting the validity of the data. Ethics committees need to consider this issue carefully.Revisión por pare

Three-dimensional photoacoustic imaging and inversion for accurate quantification of chromophore distributions

Photoacoustic tomography can, in principle, provide quantitatively accurate, high-resolution, images of chromophore distributions in 3D in vivo. However, achieving this goal requires not only dealing with the optical fluence-related spatial and spectral distortion but also having access to high quality, calibrated, measurements and using image reconstruction algorithms free from inaccurate assumptions. Furthermore, accurate knowledge of experimental parameters, such as the positions of the ultrasound detectors and the illumination pattern, is necessary for the reconstruction step. A meticulous and rigorous experimental phantom study was conducted to show that highly-resolved 3D estimation of chromophore distributions can be achieved: a crucial step towards in vivo implementation. The phantom consisted of four 580 μm diameter tubes with different ratios of copper sulphate and nickel sulphate as hemoglobin analogues, submersed in a background medium of intralipid and india ink. The optical absorption, scattering, photostability, and Grüneisen parameter were characterised for all components independently. A V-shaped imaging scanner enabled 3D imaging with the high resolution, high sensitivity, and wide bandwidth characteristic of Fabry-Pérot ultrasound sensors, but without the limited-view disadvantage of single-plane scanners. The optical beam profile and position were determined experimentally. Nine wavelengths between 750 and 1110 nm were used. The images of the chromophore concentrations were obtained using a model-based, two-step, procedure, that did not require image segmentation. First, the acoustic reconstruction was solved with an iterative time-reversal algorithm to obtain images of the initial acoustic pressure at each of the nine wavelengths for an 18×17×13 mm3 volume with 50μm voxels. Then, 3D high resolution estimates of the chromophore concentrations were obtained by using a diffusion model of light transport in an iterative nonlinear optimisation scheme. Among the lessons to be drawn from this study, one is fundamental: in order to obtain accurate estimates of chromophores (or their ratios) it is not only necessary to model the light fluence accurately, but it is just as crucial to obtain accurate estimates of the initial acoustic pressure distributions, and to account for variations in the thermoelastic efficiency (Grüneisen parameter). © (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only