Eleven-dimensional massless superparticles and matrix theory spin-orbit couplings revisited

The classical probe dynamics of the eleven-dimensional massless superparticles in the background geometry produced by N source M-momenta is investigated in the framework of N-sector DLCQ supergravity. We expand the probe action up to the two fermion terms and find that the fermionic contributions are the spin-orbit couplings, which precisely agree with the matrix theory calculations. We comment on the lack of non-perturbative corrections in the one-loop matrix quantum mechanics effective action and its compatibility with the supergravity analysis.Comment: 11 pages, Latex, no figure

Universality classes and crossover behaviors in non-Abelian directed sandpiles

We study universality classes and crossover behaviors in non-Abelian directed sandpile models, in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the algebraic decay of the grain density along the propagation direction of an avalanche. Crossover scaling behaviors are observed in the grain density due to the interplay between the toppling randomness and the parity of the threshold value. In the presence of such crossovers, we show that the broadness of the grain distribution plays a crucial role in resolving the ambiguity of the universality class. Finally, we claim that the metastable pattern analysis is important as much as the conventional analysis of avalanche dynamics.Comment: 10 pages, 7 figures, 1 table; published in PRE as the full paper of PRL v101, 218001 (2008

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Smearing Effect in Plane-Wave Matrix Model

Motivated by the usual D2-D0 system, we consider a configuration composed of flat membrane and fuzzy sphere membrane in plane-wave matrix model, and investigate the interaction between them. The configuration is shown to lead to a non-trivial interaction potential, which indicates that the fuzzy sphere membrane really behaves like a graviton, giant graviton. Interestingly, the interaction is of r^{-3} type rather than r^{-5} type. We interpret it as the interaction incorporating the smearing effect due to the fact that the considered supersymmetric flat membrane should span and spin in four dimensional subspace of plane-wave geometry.Comment: 26 pages; added referenc

Non-Quasinormal Modes and Black Hole Physics

The near-horizon geometry of a large class of extremal and near-extremal black holes in string and M theory contains three-dimensional asymptotically anti-de Sitter space. Motivated by this structure, we are led naturally to a discrete set of complex frequencies defined in terms of the monodromy at the inner and outer horizons of the black hole. We show that the correspondence principle, whereby the real part of these ``non-quasinormal frequencies'' is identified with certain fundamental quanta, leads directly to the correct quantum behavior of the near-horizon Virasoro algebra, and thus the black hole entropy. Remarkably, for the rotating black hole in five dimensions we also reproduce the fractionization of conformal weights predicted in string theory.Comment: 4 pages, revtex4; v2: reference added; v3: more references, minor typo corrected; v4: minor rewording to adjust size (ugh!); v5: some small clarifications at referees' suggestio

Euler number of Instanton Moduli space and Seiberg-Witten invariants

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.Comment: LaTeX, 34 page

N=(4,4) Type IIA String Theory on PP-Wave Background

We construct IIA GS superstring action on the ten-dimensional pp-wave background, which arises as the compactification of eleven-dimensional pp-wave geometry along the isometry direction. The background geometry has 24 Killing spinors and among them, 16 components correspond to the non-linearly realized kinematical supersymmetry in the string action. The remaining eight components are linearly realized and shown to be independent of x^+ coordinate, which is identified with the world-sheet time coordinate of the string action in the light-cone gauge. The resultant dynamical N=(4,4) supersymmetry is investigated, which is shown to be consistent with the field contents of the action containing two free massive supermultiplets.Comment: latex, 15 pages; v2: typos corrected, polished, references adde

Spectrum of Eleven-dimensional Supergravity on a PP-wave Background

We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave background. We also discuss the connection with the Kaluza-Klein zero modes of AdS_4 x S^7 background.Comment: 17 pages, no figures, LaTeX2e, typos correcte

Time-Varying Priority Queuing Models for Human Dynamics

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in the arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario.Comment: 8 pages, 6 figure