Showing papers in "Progress of Theoretical Physics in 1999"

Non-Trivial Ultraviolet Fixed Point in Quantum Gravity

Abstract: The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions (2 � d ≤ 4). It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbativelly �-expanded calculations in 2 + � gravity theory remains in d = 4. Hence it is possible that quantum gravity is an asymptotically safe theory and renormalizable in 2

Anomaly Cancellations in the Type I D9-D9 System and the USp(32) String Theory

Abstract: We check some consistency conditions for the D9-D9 system in type I string theory. The gravitational anomaly and gauge anomaly for SO(n)×SO(m) gauge symmetry are shown to be cancelled when n−m = 32. In addition, we find that a string theory with USp(n) × USp(m) gauge symmetry also satisfies the anomaly cancellation conditions. After tachyon condensation, the theory reduces to a tachyon-free USp(32) string theory, though there is no spacetime supersymmetry. ∗e-mail: sugimoto@yukawa.kyoto-u.ac.jp

An Uncertainty Relation of Space-Time

Abstract: We propose an uncertainty relation of space-time. This relation is characterized by G~T . δV , where T and δV denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of ’t Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula √ EV/G~2, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER/~ with R denoting the length scale of the system. ∗) E-mail: sasakura@gauge.scphys.kyoto-u.ac.jp 1 typeset using PTPTEX.sty

Generalised Calogero-Moser models and universal Lax pair operators

Abstract: Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H3, H4, and the dihedral group I2(m), besides the well-known ones basedon crystallographic root systems, namely those associatedwith Lie algebras. Universal Lax pair operators for all of the generalisedCalogero-Moser mod els andfor any choices of the potentials are constructedas linear combinations of the reflection operators. The consistency conditions are reduced to functional equations for the coefficient functions of the reflection operators in the Lax pair. There are only four types of such functional equations corresponding to the two-dimensional sub-root systems, A2, B2, G2, and I2(m). The root type andthe minimal type Lax pairs, d erivedin our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators, a powerful tool for solving quantum Calogero-Moser models. Generalised Calogero-Moser models are integrable many-particle dynamical systems based on finite reflection groups. Finite reflection groups include the dihedral groups I2(m) and H3 and H4 together with the Weyl groups of the root systems associated with Lie algebras, called crystallographic root systems. Integrability of classical Calogero-Moser models based on the crystallographic root systems 1), 2) is shown in terms of Lax pairs. The root and the minimal type Lax pairs derived in our previous papers 3) provide a universal framework for these Calogero-Moser models, including those based on exceptional root systems and the twisted models. On the other hand, a theory of classical integrability for the models based on non-crystallographic root systems has been virtually non-existent. This is in sharp contrast with the quantum counterpart. Dunkl operators, which are useful for solving quantum Calogero-Moser models, were first explicitly constructed for the models based on the dihedral groups. 4)

Polarized Structure Functions in QCD

Abstract: Hadron spin physics is now one of the most active fields of physics. Especially in the last ten years, great progress has been made both theoretically and experimentally that has considerably improved our knowledge of the spin structure of nucleons. We review the nucleon’s polarized structure functions fromthe viewpoint of factorization theorem s and the gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions, which are relevant to inclusive lepto- and hadro-production. We give a detailed analysis of these spin-dependent distribution functions at the twist-2 and twist-3 level, and present various properties and relations satisfied by the parton distributions, which can be derived directly fromQCD. We em phasize unique features of higher twist distributions, and the role of the QCD equations of motion to derive their sensitivity to the quark-gluon correlation and their anomalous dimensions for Q 2 -evolution.

Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

Abstract: An analytic solution of the Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter geometries is presented, and the properties of this solution are examined. In particular, we show that our solution satisfies the Teukolsky-Starobinsky identities explicitly and fix the relative normalization between solutions with spin weights s ands. alytic solution of the perturbation equation of massless fields in Kerr geometries which is commonly called the Teukolsky equation. 3) This solution enabled us to in- vestigate various properties of black holes analytically, 4) the scattering problem of a particle emitted in a black hole, an analytical expression for the absorption rate by a Kerr black hole, which was one of the main interests of Chandrasekhar, 5) and the Teukolsky-Starobinsky identities. Our solution is expressed in the form of a series of hypergeometric functions and Coulombwave functions. The coefficients of this series are determined b y solving three-term recurrence relations. Two series have different convergence regions, and they are matched in the region where both series converge. This method turns out to be quite powerful in practical calculations and is successfully applied to examine gravitational waves from a binary in a post-Newtonian expansion; to construct the template of the gravitational wave emitted from a particle moving around a Kerr black hole 6) and the rate of absorption of a gravitational wave by the black hole. 7) In a previous paper, 8) Suzuki, Takasugi and Umetsu extended this method to solve the perturbation equations of massless fields (the Teukolsky equation) in Kerr- de Sitter and Kerr-Newman-de Sitter geometries. We found transformations such that both the angular and the radial equations are reduced to Heun's equation. 9) The solution of Heun's equation is expressed in the form of a series of hypergeometric functions, and its coefficients are determined by three-term recurrence relations, similarly to the Kerr geometry case. It should be noted that electromagnetic fields and gravitational fields couple to each other in Kerr-Newman-de Sitter geometries and do not obey the equation we considered there, although the fields obey the

Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator

Abstract: The chiral Jacobian, which is defined with Neuberger’s overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.

Neutrino Masses in E6 Unification

Abstract: We show that neutrino masses with large mixing between νμ and ντ are naturally reproduced in a supersymmetric E6 grand unification model with an anomalous U(1)X symmetry. We propose a simple scenario which incorporates a novel mechanism called ‘E-twisting’ by which all the characteristic features of the fermion mass matrices, not only the quark/lepton Dirac masses but also the neutrino’s Majorana masses, can be reproduced despite the fact that all the members in 27 of each generation are assigned a common U(1)X charge.

Fully General Relativistic Simulation of Merging Binary Clusters Spatial Gauge Condition

Abstract: We have carried out simulations of the coalescence between two relativistic clusters of collisionless particles using a 3D numerical relativity code. We have adopted a new spatial gauge condition obtained by slightly modifying the minimum distortion gauge condition proposed by Smarr and York and resulting in a simpler equation for the shift vector. Using this gauge condition, we have performed several simulations of the merger between two identical clusters in which we have varied the compaction, the type of internal motion in the clusters, and the magnitude of the orbital velocity. As a result of the coalescence, either a new rotating cluster or a black hole is formed. In the case in which a black hole is not formed, simulations could be carried out for a time much longer than the dynamical time scale, and the resulting gravitational waveforms were calculated fairly accurately: In these cases, the amplitude of gravitational waves emitted can be $\sim 10^{-18}(M/10^6M_{\odot})$ at a distance 4000Mpc, and $\sim 0.5%$ of the rest mass energy may be dissipated by the gravitational wave emission in the final phase of the merger. These results confirm that the new spatial gauge condition is promising in many problems at least up to the formation of black holes. In the case in which a black hole is formed, on the other hand, the gauge condition seems to be less adequate, but we suggest a strategy to improve it in this case. All of the results obtained confirm the robustness of our formulation and the ability of our code for stable evolution of strong gravitational fields of compact binaries.

The Role of Domain Walls on the Vortex Creep Dynamics in Unconventional Superconductors

Abstract: We investigate the influence of domain walls on the vortex dynamics in superconductors with multi-component order parameters. We show that, due to their complex structure domain walls can carry vortices with fractional flux quanta. The decay of conventional vortices into fractional ones on domain walls is examined. This decay presents an extraordinarily strong pinning mechanism for vortices and turns domain walls occupied with pinned fractional vortices into efficient barriers for the vortex motion. Therefore, domain walls can act as fences for the flux flow, preventing the decay of the remnant magnetic flux enclosed by them. Furthermore, the consequences of this property of domain walls on the vortex dynamics are discussed in connection with observed noise in the hysteresis cycle, using the Bean model of the critical vortex state. Based on this picture experimental data in the unconventional superconductors UPt3 ,U 1�xThxBe13 and Sr2RuO4 are interpreted.

Calogero-Moser Models. II Symmetries and Foldings

Abstract: Universal Lax pairs (the root type and the minimal type) are presented for CalogeroMoser models based on simply laced root systems, including E8. They exist with and without spectral parameters and they work for all of the four choices of potentials: the rational, trigonometric, hyperbolic and elliptic. For the elliptic potential, the discrete symmetries of the simply laced models, originating from the automorphism of the extended Dynkin diagrams, are combined with the periodicity of the potential to derive a class of CalogeroMoser models known as the ‘twisted non-simply laced models’. For untwisted non-simply laced models, two kinds of root type Lax pairs (based on long roots and short roots) are derived which contain independent coupling constants for the long and short roots. The BCn model contains three independent couplings, for the long, middle and short roots. The G2 model based on long roots exhibits a new feature which deserves further study.

Matter Representations and Gauge Symmetry Breaking via Compactified Space

Abstract: We study dynamical gauge symmetry breaking via compactified space in the framework of SU(N )gauge theory in M d−1 × S 1 (d =4 , 5, 6)space-time. In particular, we study in detail the gauge symmetry breaking in SU(2)and SU(3)gauge theories when the models contain both fundamental and adjoint matter. As a result, we find that any pattern of gauge symmetry breaking can be realized by selecting an appropriate set of numbers (Nf ,N ad)in these cases. This is achieved without tuning boundary conditions of the matter fields. As a by-product, in some cases we obtain an effective potential which has no curvature at the minimum, thus leading to massless Higgs scalars, irrespective of the size of the compactified space.

Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice

Abstract: Luscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative)sector in infinite volume, is reinterpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent. The real part of the effective action is simply one-half that of the Dirac fermion and, when the Dirac operator behaves properly in the continuum limit, the imaginary part in this limit reproduces the η-invariant. In the present note, we give a reinterpretation of Luscher's formulation in Ref. 7) in terms of the "lattice covariant regularization" proposed in the past by the present author and a collaborator. 15),16) This reinterpretation is possible at least in the vacuum sector (implying that the Dirac operator has no zero modes and the inverse of the Dirac operator exists) in infinite lattice volume (for which the results of Ref. 14) can be used straightforwardly). Although the most interesting part of Ref. 7) is the analysis of the topological sector in a finite lattice volume, we will clarify some of properties of the formulation in this simpler situation, by giving a one parameter integral representation of Luscher's effective action. Now, in the scheme of Refs. 15) and 16), the primarily-defined quantity is the variation of the effective action with respect to the gauge field, "the gauge current".

Gravitational Radiation from a Naked Singularity: Odd-Parity Perturbation

Abstract: A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the even-parity mode of gravitational waves from a naked singularity of the LemaˆotreTolman-Bondi spacetime. The wave equations for gravitational waves are solved by numerical integration using the single null coordinate. The result implies that the metric perturbation grows when it approaches the Cauchy horizon and diverges there, although the naked singularity is not a strong source of even-parity gravitational radiation. Therefore, the Cauchy horizon in this spacetime should be unstable with respect to linear even-parity perturbations.

J/ψ-Nucleon Scattering Length and In-Medium Mass Shift of J/ψ in QCD Sum Rule Analysis

Abstract: We calculate the spin-averaged J/ψ-nucleon scattering length aJ/ψ by directly applying the QCD sum rule to the J/ψ-N forward scattering amplitude. Our result, aJ/ψ = −0.10± 0.02 fm, implies the possibility of bound states with nuclei, though the force is weaker than that of the light vector mesons (ρ, ω, φ)-N cases. Up to dimension-4 gluonic operators, we evaluate the scattering length with a twist-2 contribution. This increases the absolute value of the scattering length by about 30%. If we apply aJ/ψ to the effective mass of J/ψ in nuclear matter on the basis of the linear density approximation, it exhibits very slight decrease (4–7 MeV) at normal matter density.

Many brane extension of the Randall-Sundrum solution

Abstract: Recently, Randall and Sundrum proposed a static solution to the Einstein equations in 5 spacetime dimensions with two 3-branes located at the fixed points of S 1 /Z2 to solve the hierarchy problem. We extend the solution and construct static and also inflationary solutions to the Einstein equations in 5 spacetime dimensions, one of which is compactified on S 1 , with any number of 3-branes whose locations are taken to be arbitrary. We discuss how the hierarchy problem can be explained in our model. 1. Introduction Recently, Randall and Sundrum 1) proposed a new interesting mechanism with a single small extra dimension for solving the hierarchy problem between the Planck scale and the weak scale. A key ingredient ofthis mechanism is that the metric is not factorizable and that the 4-dimensional metric is multiplied by a warp factor which is a rapidly changing function of the extra dimension. They explicitly constructed such a solution to the Einstein equations in 5 spacetime dimensions, one ofwhich is compactified on S 1 /Z2, with two 3-branes located at the fixed points of S 1 /Z2. For a solution to exist, it is crucial to take into account the effect ofthe branes on the bulk gravitational metric. In the Randall-Sundrum model, the number of3-branes is 2 and the locations are taken to be the fixed points of S 1 /Z2. Although this setup is motivated by recent developments in string and M-theory, 2) it would be ofinterest to construct new solutions to the 5-dimensional Einstein equations with many 3-branes. In this paper, we explicitly construct solutions with an arbitrary number of3-branes which are put at arbitrary positions in the direction ofthe extra dimension. Our motivation f this is threefold. First, it is known that any number of parallel D-branes can be put at arbitrary positions and that the gauge dynamics depend on the distances ofmultiple D-branes. Thus, it is physically meaningful to construct solutions corresponding to many 3-branes put at arbitrary positions. Second, many-brane configurations could explain other hierarchy problems, such as the fermion mass hierarchy. The origi

Arrival times in quantum theory from an irreversible detector model

Abstract: We investigate a detector scheme designed to measure the arrival of a particle at x = 0 during a finite time interval. The detector consists of a two-state system that undergoes a transition from one state to the other when the particle crosses x = 0, and possesses the realistic feature that it is effectively irreversible as a result of being coupled to a large environment. The probabilities for crossing or not crossing x = 0 thereby derived coincide with earlier phenomenologically proposed expressions involving a complex potential. The probabilities are compared with similar previously proposed expressions involving sums over paths, and a connection with time operator approaches is also indicated.

Three-Dimensional Black Holes and Liouville Field Theory.

Abstract: diffS 1 ±. Its quantization provides unitary irreducible representations of the Virasoro algebra, in which the state of the black hole becomes primary. To make the quantization complete, holonomies, the global degrees of freedom, are taken into account. By an identification of these topological operators with zero modes of the Liouville field, the aforementioned unitary representations are shown, as long as c � 1, to be the Hilbert space of this two-dimensional conformal field theory. This conformal field theory, living on the cylinder at infinity of the black hole and having continuous spectra, can recognize the outer horizon only as a one-dimensional object in SL2( ) and realize it as insertions of the corresponding vertex operator. Therefore it cannot be a conformal field theory on the horizon. Two possible descriptions of the horizon conformal field theory are proposed.

Calogero-Moser Models. IV ---Limits to Toda Theory---

Abstract: Calogero-Moser models and Toda models are well-known integrable multi-particle dynamical systems based on root systems associated with Lie algebras. The relation between these two types of integrable models is investigated at the levels of the Hamiltonians and the Lax pairs. The Lax pairs of Calogero-Moser models are specified by the representations of the reflection groups, which are not the same as those of the corresponding Lie algebras. The latter specify the Lax pairs of Toda models. The Hamiltonians of the elliptic Calogero-Moser models tend to those of Toda models as one of the periods of the elliptic function goes to infinity, provided the dynamical variables are properly shifted and the coupling constants are scaled. On the other hand most of Calogero-Moser Lax pairs, for example, the root type Lax pairs, do not have a consistent Toda model limit. The minimal type Lax pairs, which corresponds to the minimal representations of the Lie algebras, tend to the Lax pairs of the corresponding Toda models.

Possible classification of the chiral scalar sigma nonet

Abstract: We recently observed the iso-singlet scalar σ(600)-particle and the iso-doublet scalar κ(900)-particle, through the re-analyses of ππ- and Kπ-scattering phase shifts, respectively. First, assuming the two iso-singlet states, the σ(600) and the established f0(980), being the

Calogero-Moser models. III: Elliptic potentials and twisting

Abstract: Universal Lax pairs of the root type with spectral parameter and independent coupling constants for twisted non-simply laced Calogero-Moser models are constructed. Together with the Lax pairs for the simply laced models and untwisted non-simply laced models presented in two previous papers, this completes the derivation of universal Lax pairs for all of the Calogero-Moser models based on root systems. As for the twisted models based on Bn, Cn and BCn root systems, a new type of potential term with independent coupling constants can be added without destroying integrability. They are called extended twisted models. All of the Lax pairs for the twisted models presented here are new, except for the one for the F4 model based on the short roots. The Lax pairs for the twisted G2 model have some novel features. Derivation of various functions, twisted and untwisted, appearing in the Lax pairs for elliptic potentials with the spectral parameter is provided. The origin of the spectral parameter is also naturally explained. The Lax pairs with spectral parameter, twisted and untwisted, for the hyperbolic, the trigonometric and the rational potential models are obtained as degenerate limits of those for the elliptic potential models.

Hadronic Weak Decays of Λb Baryon in the Covariant Oscillator Quark Model

Abstract: Cabibbo allowed two-body hadronic weak decays of Λb baryons are analyzed in the factorization approximation. We use the covariant oscillator quark model to evaluate the heavy → heavy and heavy → light form factors. When applied in the heavy quark limit, our form factors satisfy all the constraints imposed by heavy quark symmetry. The decay rates and up-down asymmetries for Λb baryon decaying into Λc + P (V ) are calculated. It is found that the up-down asymmetry is negative in all these decay modes. Furthermore, the prediction Br(Λb → Λ + J/ψ )=2 .49 × 10 −4 is consistent with the recent experimental data. Finally it is pointed out that the CKM-Wolfenstein parameter ρ 2 + η 2 , where η is the CP phase, can be determined from the ratio of the widths Λb → Λ ¯ D 0 and Λb → ΛJ/ψ, independent of the QCD parameter. The value of (ρ 2 + η 2 ) 1/2 calculated in our model agrees very well with the value recently predicted by Rosner.

Superfluidity of Λ-Hyperons Admixed in Neutron Star Cores ∗)

Abstract: Λ-superfluidity in a hyperon core of neutron stars is studied with a realistic approach. It is found that Λ-superfluid exists in a restricted density region ρ (ρt-ρd) with ρt 2ρ0 (ρ0 being the nuclear density) and ρd (2.6-4.6)ρ0 depending on the pairing interaction and the hyperon core model. This restriction suggests that neutron stars compatible with hyperon cooling would be not so massive. Introduction Study on the superfluidity of hyperons admixed in neutron star cores is of increasing interest not only with regard to many-body problems in hadronic matter including exotic components but also to the cooling scenario of neutron stars inferred from surface temperature observations. It has been suggested that some neutron stars are cooled much more rapidly than expected from the standard cool- ing scenario (i.e., modified URCA process; e.g., n + n → p + n + e − +¯ νe, and the inverse process), and a more efficient cooling mechanism is needed. 2) In this con- nection, so-called "hyperon cooling", 3) associated with neutrino emission processes as of the β-decay type including hyperons (Λ → p + e − +¯ νe ,Σ − → Λ + e − +¯ νe, etc.), provides one of the rapid cooling mechanisms. The direct action of such rapid cooling, however, leads to a surface temperature much lower than that observed. This demands some suppression mechanism, most naturally hyperon superfluidity, to control the cooling rate. Therefore it becomes of special interest to investigate whether hyperon superfluidity is possible in the hyperon-mixed phase believed to exist in neutron star cores. In this paper, as a typical example of hyperon superfluidity, we focus attention on Λ-hyperon pairing, since at present the uncertainty in the ΛΛ interaction is relatively small due to the information from various experimental data (especially, the available data from double Λ hypernuclei) and theoretical studies. Very recently, Balberg and Barnea 4) studied this subject by using an effective ΛΛ interaction ˜ VΛΛ for ΛΛ pairing interaction. However, their approach using an effective interaction for the pairing problem is not justified, as shown later. Moreover, the ˜ VΛΛ they used 5) is based on the G-matrix calculations for two Λ particles immersed in symmetric nuclear matter, but such situation is basically different from the actual one of the hyperon- mixed phase composed of neutrons as a dominant component, protons, Λ-particles and other hyperons. In addition, the effective mass they used for Λ is not suitable.

Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

Abstract: The critical dynamics of the chiral symmetry breaking induced by a gauge interaction is examined in the Wilson renormalization group framework in comparison with the SchwingerDyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalization group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.

Dynamical Effects on the 9Li-n Interaction Induced by Pauli Blocking of the Jπ = 0+ Pairing Correlation

Abstract: The 9 Li-n interaction is discussed based on the idea of the Pauli blocking for the J π =0 + neutron pairing correlation in the 9 Li core due to the presence of the last valence neutron. The present studies are developed in a framework of the microscopic coupled-channel model for { 9 Li((0p3/2) 4 )+ n} + { 9 Li((0p3/2) 2 (0p1/2) 2 )+ n} + { 9 Li((0p3/2) 2 (1s0d) 2 )+ n}. The channel of the present model consists of the last valence neutron coupled with a 9 Li configurational state connected by the J π =0 + pairing interaction. Due to the presence of the valence neutron in the 0p1/2 orbital, the (0p3/2) 2 → (0p1/2) 2 jump in the 9 Li core is prevented. Thus, the p1/2-orbital neutron states experience a strong repulsive effect due to the lack of the configuration mixing between (0p3/2) 4 and (0p3/2) 2 (0p1/2) 2 , and its energy rises up significantly. In contrast to this, the sd-orbital neutron imparts a very weak effect on the configuration mixing. As a result, the s1/2-orbital state is obtained in the vicinity of the threshold as a bound state or virtual resonance for the 9 Li-n interaction which reproduces 1 + (Sn = −0.42 MeV) and 2 + (Sn = −0.82 MeV) states consistently with experimental data observed by Bohlen et al. The effective 9 Li-n potential which has the strong parity dependence deduced fromthe present coupled-channel calculation is discussed to be very promising for studying the halo structure of 11 Li within the 9 Li + n + n model.

Kepler Rotation Effects on the Binary-Lens Microlensing Events

Abstract: We investigate the effects of the Kepler rotation of lens binaries on the binary-microlensing events towards the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). It is found that the rotation effects cannot always be neglected when the lens binaries are in the LMC disk or the SMC disk, i.e., when they are self-lensing. Therefore we suggest that it will be necessary to consider the rotation effects in the analyses of the coming binary events if the microlensing events towards the halo are self-lensing. As an example, we reexamine the MACHO LMC-9 event, in which the slow transverse velocity of the lens binary suggests a microlensing event in the LMC disk. From a simple analysis, it is shown that the lens binary with total mass $\sim 1M_{\odot}$ rotates by more than $\sim 60^{\circ}$ during the Einstein radius crossing time. However, the fitting of MACHO LMC-9 with an additional parameter, the rotation period, shows that the rotation effects are small, i.e., the projected rotation angle is only $\sim 5.9^{\circ} (M/M_{\odot})^{1/4}$ during the Einstein radius crossing time. This contradiction can be settled if the physical parameters, such as the mass and the velocity, are different in this event, the binary is nearly edge-on, or the binary is very eccentric, though definite conclusions cannot be drawn from this single event. If the microlensing events towards the halo are due to self-lensing, binary-events for which the rotation effects are important will increase and stronger constraints on the nature of the lenses will be obtained.

Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. I : Elliptic Billiard

Abstract: We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of the circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We show that the circular disk limit of the diameter-orbit contribution is also reached through contributions from closed (periodic and non-periodic) orbits of hyperbolic type with an even number of reflections from the boundary. We obtain the Maslov indices depending on deformation and energy in terms of the phases of the complex error and Airy functions. We find enhancement of the amplitudes near the common bifurcation points of both short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones.

Branes in Type 0/Type II Duality

Abstract: We derive relations between type 0 and type II D-brane configurations under the Tduality suggested by Bergman and Gaberdiel and confirm that the massless fields on Dbranes are identical to those on the dual D-brane configurations. Furthermore, we discuss dualities of type 0 and type II NS5-branes and find that the dual of an unwrapped type 0 NS5-brane is a Kaluza-Klein monopole with non-supersymmetric blow up modes.

3d numerical simulation of black hole formation using collisionless particles : triplane symmetric case

Abstract: We have constructed a numerical code for 3D numerical relativity with which we can investigate black hole formation processes for a wide variety of problems. We adopt a standard 3+1 formalism for the evolution of geometric variables incorporating a swarm of collisionless particles as a source of the energy momentum tensor. In order to determine black hole formation, we also incorporate an apparent horizon finder which was recently developed. Assuming triplane symmetries with respect to x-y, y-z and z-x planes, we have performed a variety of simulations for black hole formation, such as the collapse of triaxial ellipsoids, collapse of spheroids of co-rotating and counter-rotating particles, and head-on collision of two nearly equilibrium spherical clusters, as well as test-bed simulations including spherical symmetric dust collapse. We present numerical results and demonstrate that using our numerical code, we can investigate black hole formation in these problems fairly accurately.