N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX

Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory

It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.Comment: 31 pages, published versio

Vortex core transitions in superfluid 3He in globally anisotropic aerogels

Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid 3He and aerogel structure.Comment: 7 pages, 6 figures Text was changed. Resubmitted versio

Testing new physics with the electron g-2

We argue that the anomalous magnetic moment of the electron (a_e) can be used to probe new physics. We show that the present bound on new-physics contributions to a_e is 8*10^-13, but the sensitivity can be improved by about an order of magnitude with new measurements of a_e and more refined determinations of alpha in atomic-physics experiments. Tests on new-physics effects in a_e can play a crucial role in the interpretation of the observed discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large class of models, new contributions to magnetic moments scale with the square of lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in which this scaling is violated and larger effects in a_e are expected. In such models the value of a_e is correlated with specific predictions for processes with violation of lepton number or lepton universality, and with the electric dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin note: substantial text overlap with arXiv:1007.088

Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

This paper presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we have evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16 (58)(\alpha/\pi)^5. We have also improved the eighth-order contribution obtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependent contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times 10^{-12}. The improved value of the fine-structure constant \alpha^{-1} = 137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement of a_e.Comment: 4 pages, 2 figures. Some numbers are slightly change

Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations

The superpotential in the Landau-Ginzburg construction of solutions to the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations is modified to include logarithmic terms. This results in deformations - quadratic in the deformation parameters- of the normal prepotential solutions of the WDVV equations. Such solutions satisfy various pseudo-quasi-homogeneity conditions, on assigning a notional weight to the deformation parameters. These solutions originate in the so-called `water-bag' reductions of the dispersionless KP hierarchy. This construction includes, as a special case, deformations which are polynomial in the flat coordinates, resulting in a new class of polynomial solutions of the WDVV equations

Fermions at unitarity and Haldane Exclusion Statistics

We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate, the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane-Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with experiment, and also with other published work.Comment: 4 pages, 1 postscript figur

Off shell κ\kappa-symmetry of the superparticle and the spinning superparticle

The spinorial local world-line $\kappa$-symmetry of the covariant Brink-Schwarz formulation of the 4-$D$ superparticle is abelian in an off-shell phase-space formulation. The result is shown to generalize to the extended spinorial transformations of the spinning superparticle.Comment: 9 pages, no fig