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

The Knight Who Saved the Shark

Reaching one’s goals is never an individual effort. I enrolled at NSU in the year 2000, joining the Men’s soccer team and pursuing a career in sports medicine. High school was easy, managing being a student athlete did not pose many challenges. I could study for an exam the night before and do quite well on it. After getting a 68% on my first biology test in college, I quickly realized this method would no longer work. Developing a new study strategy and keeping up with the demands of being a full time athlete and social life was not easy. I struggled with it so much that I made up my mind that I would change my major from Biology to Business. As I sat in Dr. Robert Pomeroy’s office (chemistry professor) explaining my decision, he gave me a firm look and said: “I am not going to let you quit.” I was shocked. For the next 4-6 months I went to his office 2-3 times per week to go over chemistry problems. He challenged me to think of a test as a soccer game. With time, not only chemistry but all my grades went up. Now that I have accomplished my goal of becoming a sports medicine physician, I realize Dr. Pomeroy’s real chemistry lesson was how to develop the work ethic face challenges head on and not let them impede your career dreams

Thermodynamics of the QCD plasma and the large-N limit

The equilibrium thermodynamic properties of the SU(N) plasma at finite temperature are studied non-perturbatively in the large-N limit, via lattice simulations. We present high-precision numerical results for the pressure, trace of the energy-momentum tensor, energy density and entropy density of SU(N) Yang-Mills theories with N=3, 4, 5, 6 and 8 colors, in a temperature range from 0.8T_c to 3.4T_c (where T_c denotes the critical deconfinement temperature). The results, normalized according to the number of gluons, show a very mild dependence on N, supporting the idea that the dynamics of the strongly-interacting QCD plasma could admit a description based on large-N models. We compare our numerical data with general expectations about the thermal behavior of the deconfined gluon plasma and with various theoretical descriptions, including, in particular, the improved holographic QCD model recently proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description for the QCD plasma in a phenomenologically interesting temperature range where the system, while still strongly-coupled, approaches a `quasi-conformal' regime characterized by approximate scale invariance. Finally, we perform an extrapolation of our results to the N to $\infty$ limit.Comment: 1+38 pages, 13 eps figures; v2: added reference

Separation of Cultivars of Soybeans by Chemometric Methods Using Near Infrared Spectroscopy.

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Calculation of the energetics of water incorporation in majorite garnet

Interpretation of lateral variations in upper mantle seismic wave speeds requires constraints on the relationship between elasticity and water concentration at high pressure for all major mantle minerals, including the garnet component. We have calculated the structure and energetics of charge-balanced hydrogen substitution into tetragonal MgSiO3 majorite up to P = 25 GPa using both classical atomistic simulations and complementary first-principles calculations. At the pressure conditions of Earth’s transition zone, hydroxyl groups are predicted to be bound to Si vacancies (o) as the hydrogarnet defect, [oSi+4OHO]X, at the Si2 tetrahedral site or as the [oMg+2OHO]X defect at the octahedral Mg3 site. The hydrogarnet defect is more favorable than the [oMg+2OHO]X defect by 0.8–1.4 eV/H at 20 GPa. The presence of 0.4 wt% Al2O3 substituted into the octahedral sites further increases the likelihood of the hydrogarnet defect by 2.2–2.4 eV/H relative to the [oMg+2OHO]X defect at the Mg3 site. OH defects affect the seismic ratio, R = dlnvs/dlnvp, in MgSiO3 majorite (?R = 0.9–1.2 at 20 GPa for 1400 ppm wt H2O) differently than ringwoodite at high pressure, yet may be indistinguishable from the thermal dlnvs/dlnvp for ringwoodite. The incorporation of 3.2 wt% Al2O3 also decreases R(H2O) by ~0.2–0.4. Therefore, to accurately estimate transition zone compositional and thermal anomalies, hydrous majorite needs to be considered when interpreting seismic body wave anomalies in the transition zone

Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory

We show how Monte Carlo approach can be used to study the double scaling limit in matrix models. As an example, we study a solvable hermitian one-matrix model with the double-well potential, which has been identified recently as a dual description of noncritical string theory with worldsheet supersymmetry. This identification utilizes the nonperturbatively stable vacuum unlike its bosonic counterparts, and therefore it provides a complete constructive formulation of string theory. Our data with the matrix size ranging from 8 to 512 show a clear scaling behavior, which enables us to extract the double scaling limit accurately. The ``specific heat'' obtained in this way agrees nicely with the known result obtained by solving the Painleve-II equation with appropriate boundary conditions.Comment: 15 pages, 10 figures, LaTeX, JHEP3.cls; references added, typos correcte

A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework

We propose a gauge-independent mechanism for the area-law behavior of Wilson loop expectation values in terms of worldsheets spanning Wilson loops interacting with the spin foams that contribute to the vacuum partition function. The method uses an exact transformation of lattice-regularized Yang-Mills theory that is valid for all couplings. Within this framework, some natural conjectures can be made as to what physical mechanism enforces the confinement property in the continuum (weak coupling) limit. Details for the SU(2) case in three dimensions are provided in a companion paper.Comment: 16 pages, 4 figure

On the effective string spectrum of the tridimensional Z(2) gauge model

We study the Z(2) lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance $r \approx 10/\sqrt{\sigma}$. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.Comment: 31 pages, 14 figure

Polyakov Loops in Strongly-Coupled Plasmas with Gravity Duals

We study the properties of the Polyakov loop in strongly-coupled gauge plasmas that are conjectured to be dual to five dimensional theories of gravity coupled to a nontrivial single scalar field. We find a gravity dual that can describe the thermodynamic properties and also the expectation value of the Polyakov loop in the deconfined phase of quenched SU(3) QCD up to $3T_c$.Comment: 7 pages, 2 figures, talk presented at the International Conference on Strangeness in Quark Matter, Buzios, Rio de Janeiro, Brazil, Sept. 27 - oct. 2, 200