We discuss a model in which the fundamental scale of gravity is restricted to 10 −3 eV. An observable modification of gravity occurs simultaneously at the Hubble distance and at around 0.1 mm. These predictions can be tested both by the tabletop experiments and by cosmological measurements. The model is formulated as a brane-world theory embedded in a space with two or more infinite-volume extra dimensions. Gravity on the brane reproduces the four-dimensional laws at observable distances but turns to the high-dimensional behavior at larger scales. To determine the crossover distance we smooth out the singularities in the Green's functions by taking into account softening of the graviton propagator at energies above the fundamental scale. This is due to the high-dimensional operators which are suppressed by the fundamental scale. We find that irrespective of the precise nature of microscopic gravity the ultraviolet and infrared scales of gravity-modification are rigidly correlated. This fixes the fundamental scale of gravity at 10 −3 eV. The result persists for nonzero thickness branes.

We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kähler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N = 2 field theory includes an auxiliary N = 1 quantum mechanics, Witten's index of which counts the number of the BPS particles. † Permanent address

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N -body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N + 1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N + n)!/(N !n!); (iv) the energy-reflection symmetry of the parent system is preserved.

We study the Abrikosov-Nielsen-Olesen string in N = 2 supersymmetric QED with N = 2-preserving superpotential, in which case the Abrikosov string is found to be 1/2-BPS saturated. Adding a quadratic small perturbation in the superpotential breaks N = 2 supersymmetry to N = 1 supersymmetry. Then the Abrikosov string is no longer BPS saturated. The difference between the string tensions for the non-BPS and BPS saturated situation is found to be negative to the first order of the perturbation parameter.

A re-analysis of a heavy charged particle production event observed at the cloudy chamber of the Yunnan Cosmic Ray Station (YCRS) in 1972 indicates that the mysterious heavy particle may be identified as a supersymmetric (SUSY) particle produced by a bombard of a neutral SUSY cosmic ray particle on proton. Based on the assumption, following the literatures that the neutral SUSY particle which constitutes the main fraction of the cold dark matter is scalar neutrino (sneutrino) or neutralino (phqtino), we evaluate the flux of such SUSY particles which gain sufficient energies via elastic scattering with charged cosmic particles on the way to an Earth detector and the capture rates in both the sneutrino and photino cases respectively. The errors appearing in the study are briefly discussed and this work may provide a basis of designing cosmic ray detectors to search for SUSY particles from the heaven.