Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography

Unlike noncommutative space, when space and time are noncommutative, it seems necessary to modify the usual scheme of quantum mechanics. We propose in this paper a simple generalization of the time evolution equation in quantum mechanics to incorporate the feature of a noncommutative spacetime. This equation is much more constraining than the usual Schr\"odinger equation in that the spatial dimension noncommuting with time is effectively reduced to a point in low energy. We thus call the new evolution equation the spacetime bootstrap equation, the dimensional reduction called for by this evolution seems close to what is required by the holographic principle. We will discuss several examples to demonstrate this point.Comment: 15 pages, harvmac. v2: typos corrected and some changes mad

Photoproduction of Pentaquark in Feynman and Regge Theories

Photoproduction of the Theta+ pentaquark on the proton is analyzed by using an isobar and a Regge models. The difference in the calculated total cross section is found to be more than two orders of magnitude for a hadronic form factor cut-off Lambda > 1 GeV. Comparable results would be obtained for 0.6 < Lambda < 0.8 GeV. We also calculate contribution of the Theta+ photoproduction to the GDH integral. By comparing with the current phenomenological calculation, it is found that the GDH sum rule favors the result obtained from Regge approach and isobar model with small Lambda.Comment: 5 pages, 5 figures, submitted to Phys.Rev.C as a Rapid Communicatio

Temporal variability in early afterglows of short gamma-ray bursts

The shock model has successfully explained the observed behaviors of afterglows from long gamma-ray bursts (GRBs). Here we use it to investigate the so-called early afterglows from short GRBs, which arises from blast waves that are not decelerated considerably by their surrounding medium. We consider a nearby medium loaded with $e^{\pm}$ pairs (Beloborodov 2002). The temporal behaviors show first a soft-to-hard spectral evolution, from the optical to hard X-ray, and then a usual hard-to-soft evolution after the blast waves begin to decelerate. The light curves show variability, and consist of two peaks. The first peak, due to the pair effect, can be observed in the X-ray, though too faint and too short in the optical. The second peak will be easily detected by {\it Swift}. We show that detections of the double-peak structure in the light curves of early afterglows are very helpful to determine all the shock parameters of short GRBs, including both the parameters of the relativistic source and the surroundings. Besides, from the requirement that the forward-shock emission in short GRBs should be below the BATSE detection threshold, we give a strong constraint on the shock model parameters. In particular, the initial Lorentz factor of the source is limited to be no more than $\sim 10^3$, and the ambient medium density is inferred to be low, n\la 10^{-1} cm$^{-3}$.Comment: 5 pages, 1 figure, minor changes to match the publish in MNRA

Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

A Two-Tiered Correlation of Dark Matter with Missing Transverse Energy: Reconstructing the Lightest Supersymmetric Particle Mass at the LHC

We suggest that non-trivial correlations between the dark matter particle mass and collider based probes of missing transverse energy H_T^miss may facilitate a two tiered approach to the initial discovery of supersymmetry and the subsequent reconstruction of the LSP mass at the LHC. These correlations are demonstrated via extensive Monte Carlo simulation of seventeen benchmark models, each sampled at five distinct LHC center-of-mass beam energies, spanning the parameter space of No-Scale F-SU(5).This construction is defined in turn by the union of the Flipped SU(5) Grand Unified Theory, two pairs of hypothetical TeV scale vector-like supersymmetric multiplets with origins in F-theory, and the dynamically established boundary conditions of No-Scale Supergravity. In addition, we consider a control sample comprised of a standard minimal Supergravity benchmark point. Led by a striking similarity between the H_T^miss distribution and the familiar power spectrum of a black body radiator at various temperatures, we implement a broad empirical fit of our simulation against a Poisson distribution ansatz. We advance the resulting fit as a theoretical blueprint for deducing the mass of the LSP, utilizing only the missing transverse energy in a statistical sampling of >= 9 jet events. Cumulative uncertainties central to the method subsist at a satisfactory 12-15% level. The fact that supersymmetric particle spectrum of No-Scale F-SU(5) has thrived the withering onslaught of early LHC data that is steadily decimating the Constrained Minimal Supersymmetric Standard Model and minimal Supergravity parameter spaces is a prime motivation for augmenting more conventional LSP search methodologies with the presently proposed alternative.Comment: JHEP version, 17 pages, 9 Figures, 2 Table

Spontaneous and Superfluid Chiral Edge States in Exciton-Polariton Condensates

We present a scheme of interaction-induced topological bandstructures based on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We predict theoretically that this scheme allows the engineering of topological gaps, without requiring a magnetic field or strong spin-orbit interaction (transverse electric-transverse magnetic splitting). Under non-resonant pumping, we find that an initially topologically trivial system undergoes a topological transition upon the spontaneous breaking of phase symmetry associated with polariton condensation. Under resonant coherent pumping, we find that it is also possible to engineer a topological dispersion that is linear in wavevector -- a property associated with polariton superfluidity.Comment: 6 pages, 4 figure