Showing papers in "Progress of Theoretical Physics in 2000"
199 citations
TL;DR: In this paper, the notion of a space-time uncertainty principle in string theory is clarified and further developed, and it is shown that string theories in 10 dimensions generically exhibit a characteristic length scale which is equal to the well-known 11 dimensional Planck length.
Abstract: The notion of a space-time uncertainty principle in string theory is clarified and further developed. The motivation and the derivation of the principle are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum transfer behavior of string scattering is consistent with the space-time uncertainty principle. It is also shown that, as a consequence of this principle, string theories in 10 dimensions generically exhibit a characteristic length scale which is equal to the well-known 11 dimensional Planck length g 1/3 s
180 citations
TL;DR: In this article, a supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d = 6 superconformal tensors, which retains the dilatation gauge symmetry, so that it is a trivial gauge fixing.
Abstract: Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d = 6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.
126 citations
TL;DR: In this article, the non-commutative version of ADHM construction of instantons is studied and the mechanism of these projections is clarified in the case that the gauge group is U(1).
Abstract: The noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz, is carefully studied. Noncommutative R is described by an algebra of operators acting in a Fock space. In the ADHM construction of instantons, one looks for zero-modes of the Dirac-like operator. The feature peculiar to the noncommutative case is that these zero-modes project out some states in the Fock space. The mechanism of these projections is clarified in the case that the gauge group is U(1). In U(N) cases, it is shown in some explicit examples that projections similar to those in the U(1) cases also appear. A physical interpretation of these projections in the IIB matrix model is also discussed.
124 citations
TL;DR: In this paper, it was shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be supersymmetrised in terms of superpotentials.
Abstract: It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefunction. Since the bosonic part of each supersymmetric model is the usual quantum Calogero-Moser model, this gives a universal formula for its ground state wavefunction and energy, which is determined purely algebraically. Quantum Lax pair operators and conserved quantities for all the above Calogero-Moser models are established.
87 citations
TL;DR: In this article, Brace, Morariu and Zumino introduced new potentials which are mixture of R-R potentials and the NS-NS 2-form.
Abstract: The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions including the Chern-Simons term.
71 citations
TL;DR: In this article, a supersymmetric nonlinear sigma model is obtained from linear sigma models by imposing super-symmetric constraints, which can be expressed by D-terms and F-terms depending on the target manifolds.
Abstract: Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending on the target manifolds. Auxiliary vector superfields appear as gauge fields without kinetic terms. If there are no D-term constraints, the target manifolds are always non-compact manifolds. When all the degrees of freedom in these non-compact directions are eliminated by gauge symmetries, the target manifold becomes compact. All supersymmetric nonlinear sigma models, whose target manifolds are the hermitian symmetric spaces, are successfully formulated as gauge theories.
69 citations
TL;DR: In this article, the nucleon-nucleon interaction in the isoscalar-scalar channel using the chiral unitary approach was studied and the t-matrix of the pion-pion scattering in this channel was summed up to all orders using the B-S equation.
Abstract: We study the nucleon-nucleon interaction in the isoscalar-scalar channel using the chiral unitary approach. The t-matrix of the pion-pion scattering in this channel is summed up to all orders using the B-S equation. We find that the calculated results at long distances are close to those of the �-exchange interaction. In addition, there appears a shorter range repulsion in this channel.
60 citations
TL;DR: In this article, a new numerical code for hydrodynamic simulation of axisymmetric systems in full general relativity was constructed, and the authors investigated the effects of rotation on the criterion for prompt collapse to black holes.
Abstract: Motivated by a recent paper by the Potsdam numerical relativity group, we have constructed a new numerical code for hydrodynamic simulation of axisymmetric systems in full general relativity. In this code, we solve the Einstein field equation using Cartesian coordinates with appropriate boundary conditions. On the other hand, the hydrodynamic equations are solved in cylindrical coordinates. Using this code, we perform simulations to study axisymmetric collapse of rotating stars, which thereby become black holes or new compact stars, in full general relativity. To investigate the effects of rotation on the criterion for prompt collapse to black holes, we first adopt a polytropic equation of state, P = Kρ Γ , where P , ρ, and K are the pressure, rest mass density, and polytropic constant, with Γ =2 . In this case, the collapse is adiabatic (i.e., no change in entropy), and we can focus on the bare effect of rotation. As the initial conditions, we prepare rigidly and differentially rotating stars in equilibrium and then decrease the pressure to induce collapse. In this paper, we consider cases in which q ≡ J/M 2 g < 1, where J and Mg are the angular momentum and the gravitational mass. It is found that the criterion of black hole formation is strongly dependent on the angular momentum parameter q .F or q< 0.5, the criterion is not strongly sensitive to q; more precisely, if the rest mass is slightly larger than the maximum allowed value of spherical stars, a black hole is formed. However, for q < 1, it changes significantly: For q � 0.9, the maximum allowed rest mass becomes ∼ 70–80% larger than that for spherical stars. These findings depend only weakly on the rotational profiles given initially. We then report the results for simulations employing a Γ -law equation of state P =( Γ − 1)ρe, where e is the specific internal energy, to study effects of shock heating. We find that the effects of shock heating are particularly important for preventing prompt collapse to black holes in the case of large q [i.e., q = O(1)].
60 citations
TL;DR: In this paper, the authors give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde, and Verlin.
Abstract: We give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made and shown to reproduce the results that are obtained to this time with a different method. We further discuss continuum limits, and argue that the holographic renormalization group may describe the renormalized trajectory in the parameter space. We also clarify the relationship of the present formalism to the analysis carried out by Henningson and Skenderis.
58 citations
TL;DR: In this paper, the mass matrices for the up and down quarks and charged leptons were derived for a supersymmetric E6 grand unified model, where the SU(5) 5 ∗ components are twisted in the third generation 27.
Abstract: We study a supersymmetric E6 grand unified model in which the SU(5) 5 ∗ components are twisted in the third generation 27. Supplementing the adjoint Higgs field to a model analyzed previously, we calculate the mass matrices for the up and down quarks and charged leptons. Although the number of free parameters is less than that of observables, an overall fitting to the observed masses and mixing angles is shown to be possible. Most notably, we find two novel, parameter-independent relations between the lepton 2-3 mixing angle θμτ and the quark masses and CKM mixing angles that are in good agreement with the large lepton mixing recently observed.
TL;DR: There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions as mentioned in this paper, and the Majorana phase plays the crucial role for the stability of the maximal mixing between the second and the third generations against quantum corrections.
Abstract: There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions. In the case of two degenerate neutrinos, the physical Majorana phase plays the crucial role for the stability of the maximal flavor mixing between the second and the third generations against quantum corrections. The physical Majorana phase of $\pi$ guarantees the maximal mixing to be stable against quantum corrections, while the Majorana phase of zero lets the maximal mixing be spoiled by quantum corrections when neutrino masses are of O(eV). The continuous change of the Majorana phase from $\pi$ to 0 makes the maximal mixing be spoiled by quantum corrections with O(eV) degenerate neutrino masses. On the other hand, when there is the large mass hierarchy between neutrinos, the maximal flavor mixing is not spoiled by quantum corrections independently of the Majorana phase.
TL;DR: In this paper, the renormalization group equation (RGE) was used to analyze the neutrino flavor mixing between ν and ντ in the minimal supersymmetric standard model (MSSM) with right-handed neutrinos.
Abstract: The Superkamiokande experiment suggests large flavor mixing between νµ and ντ .W e show that both the second and third generation neutrino masses are larger than O(0. 1e V) when the mixing angle receives significant corrections from the renormalization group equa- tion (RGE). This implies that this mixing angle must be small at the right-handed neutrinos' decoupling scale when the results of the LSND experiments are correct and when the atmo- spheric neutrino anomaly is accounted for by νµ-ντ oscillation. In this paper we analyze the RGE of the neutrino flavor mixing between νµ and ντ in the minimal supersymmetric standard model (MSSM) with right-handed neutrinos.Here we take the viewpoint that the smallness of neutrino masses is accounted for by the seesaw mechanism. 7) We consider the situation that mνe is much smaller than mνµ and mντ , and we expect that the solar neutrino problem 8) is solved by the oscillation between νe and a sterile neutrino νs. 9) This situation is the so-called "four light neutrinos scenario" 10), 11) with a mass spectrum satisfying mνs ≈ mνemνµ ≈ mντ .The seesaw mechanism can also explain the results of the LSND, 12) which suggest small mixing between νµ and νe with m 2µ − m 2e ∼ 1e V 2 . †) In this mass spectrum, we find that the mixing angle between νµ and ντ undergoes significant corrections due to the renormalization group equation (RGE), and the mixing angle at high energy must be small as long as the mixing at low energy is maximal.From the viewpoint of model building, we must find a fundamental theory which predicts a small mixing angle at high energy in models which have the same
TL;DR: In this paper, an adiabatic approximation to the selfconsistent collective coordinate method is formulated in order to describe large amplitude collective motions in nuclei with pairing correlations on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion.
Abstract: An adiabatic approximation to the selfconsistent collective coordinate method is formulated in order to describe large amplitude collective motions in nuclei with pairing correlations on the basis of the time-dependent Hartree-Fock-Bogoliubov equations of motion. The basic equations are presented in a local harmonic form which can be solved in a manner similar to that of the quasiparticle RPA equations. The formalism guarantees the conservation of nucleon number expectation values. An extension to the multi-dimensional case is also discussed.
TL;DR: In this article, a new version of SU(3) non-Abelian Stokes theorem was derived by making use of the coherent state representation on the coset space SU (3)/(U(1) × U(1)) = F2, the flag space.
Abstract: We derive a new version of SU(3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space SU(3)/(U(1) × U(1)) = F2, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes theorem with the reformulation of the Yang-Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if G = SU(3) is broken by partial gauge fixing into H = U(2) just as G is broken to H = U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(2). Abelian dominance is an immediate byproduct of these results and magnetic monopole plays the dominant role in this derivation.
TL;DR: In this article, the problem of determining whether the total energy-momentum, total angular momentum and total charge are equal to the corresponding quantities of the gravitational source was examined for charged axi-symmetric solutions of gravitational field equations.
Abstract: In extended new general relativity, which is formulated as a reduction of a Poincare gauge theory of gravity whose gauge group is the covering group of the Poincare group, we study the problem of whether the total energy-momentum, total angular momentum and total charge are equal to the corresponding quantities of the gravitational source. We examine this problem for charged axi-symmetric solutions of gravitational field equations. Our main concern is the restriction on the asymptotic form of the gravitational field variables imposed by the requirement that physical quantities of the total system are equivalent to the corresponding quantities of the charged rotating source body. This requirement can be regarded as an equivalence principle in a generalized sense.
TL;DR: In this paper, the authors used the 5-dimensional spin-0 form of the Kemmer-Duffin-Petiau (KDP) equation to calculate scattering observables and deduced σTot and σReac from transmission data for K + + 6 Li, 12 C, 28 Si and 40 Ca at several momenta in the range 488-714 MeV/c.
Abstract: The 5-dimensional spin-0 form of the Kemmer-Duffin-Petiau (KDP) equation is used to calculate scattering observables [elastic differential cross sections (dσ/dΩ), total cross sections (σTot ), and total reaction cross sections (σReac)] and to deduce σTot and σReac from transmission data for K + + 6 Li, 12 C, 28 Si and 40 Ca at several momenta in the range 488– 714 MeV/c. Realistic uncertainties are generated for the theoretical predictions. These errors, mainly due to uncertainties associated with the elementary K + + nucleon amplitudes, are large, which may account for some of the disagreement between experimental and theoretical σTot and σReac. The results suggest that the K + + nucleon amplitudes need to be much better determined before further improvement in the understanding of these data can occur.
TL;DR: In this paper, a two-dimensional nonlinear nonlinear gauge theory with conjugate scalars in two dimensions was proposed. But this theory is based on a nonlinear Lie algebra (finite W algebra) or a Poisson algebra, which yields a canonical star product.
Abstract: Nonlinear gauge theory is a gauge theory based on a nonlinear Lie algebra (finite W algebra) or a Poisson algebra, which yields a canonical star product for deformation quantization as a correlator on a disk. We pursue nontrivial deformation of topological gauge theory with conjugate scalars in two dimensions. This leads uniquely to a two-dimensional nonlinear gauge theory, which implies its essential uniqueness. We also consider a possible generalization to higher dimensions.
TL;DR: In this paper, the authors studied Witten's open string field theory in the presence of a constant B field and showed that the vertices in the resulting theory have an additional factor that makes the zero modes of strings noncommutative.
Abstract: We study Witten’s open string field theory in the presence of a constant B field We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting theory has an additional factor This factor makes the zero modes of strings noncommutative This is in agreement with the results in the first-quantized formulation We also discuss the background independence of the purely cubic action derived from the above mentioned string field theory and then make a redefinition of string fields to remove the additional factor from the vertex Furthermore, we briefly discuss the supersymmetric extension of our string field theory
TL;DR: In this article, the effect of the quark substructure of N and Λ on their binding energies was examined and the charge symmetry breaking of the ΛN potential was determined and concluded to be weakly spin dependent.
Abstract: ΛΛHe are calculated to be strongly overbound compared to experiment. In relation to this well-known anomaly, we examine the effect of the quark substructure of N and Λ on their binding energies. The effect is negligible if the baryon size in which the three quarks are confined is smaller than 0.6 fm, but it becomes appreciable, particularly in 6 ΛΛHe, if the size is taken to be as large as 0.7 fm. We discuss the extent to which the nucleon subsystem in the hypernuclei changes by the addition of Λ particles. The charge symmetry breaking of the ΛN potential is phenomenologically determined and concluded to be weakly spin dependent.
TL;DR: In this paper, the authors studied the properties of the bound state (F 1, D1, D3) in IIB supergravity in three different scaling limits and the SL(2,Z) transformation of the resulting theories.
Abstract: We discuss the properties of the bound state (F1, D1, D3) in IIB supergravity in three different scaling limits and the SL(2,Z) transformation of the resulting theories. In the simple decoupling limit with finite electric and magnetic components of NS B field, the worldvolume theory is the N = 4 super Yang-Mills (SYM) and the supergravity dual is still the AdS5 × S. In the large magnetic field limit with finite electric field, the theory is the noncommutative super Yang-Mills (NCSYM), and the supergravity dual is the same as that without the electric background. We show how to take the decoupling limit of the closed string for the critical electric background and finite magnetic field, and that the resulting theory is the noncommutative open string (NCOS) with both space-time and space-space noncommutativities. It is shown that under the SL(2,Z) transformation, the SYM becomes itself with a different coupling constant, the NCSYM is mapped to a NCOS, and the NCOS in general transforms into another NCOS and reduces to a NCSYM in a special case.
TL;DR: In this article, it was shown that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value.
Abstract: This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to characterize the thermodynamic irreversibility. It is proved that this new quantity satisfies an inequality associated with the second law of thermodynamics. Based on the assumption that these systems possess the mixing property and certain large deviation properties in the thermodynamic limit, it is argued reasonably that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value. The consistency of our argument is confirmed by numerical experiments with the aid of the definition of a quantity we refer to as the excess information loss.
TL;DR: In this paper, it was shown that a rotating lens is not distinguishable from a non-rotating one, up to the first order in the gravitational constant G. The quadrupole contribution to the deflection angle is calculated for a general, extended lens object.
Abstract: It is known that the rotation of a gravitational lens affects properties of images. We consider an inverse problem: If the lens is dark, can we infer its rotation from the observed images? We find that, up to the first order in the gravitational constant G, a rotating lens is not distinguishable from a non-rotating one. The quadrupole contribution to the deflection angle is also calculated for a general, extended lens object.
TL;DR: In this paper, the SU(2) chiral sigma model was applied to neutron-rich matter in beta equilibrium, related to neutron star structure, and the maximum mass and corresponding radius of stable non-rotating neutron stars were found to be in the observational limit.
Abstract: We discuss the SU(2) chiral sigma model in the context of nuclear matter using a mean field approach at high density. In this model we include a dynamically generated isoscalar vector field and higher-order terms in the scalar field. With the inclusion of these, we reproduce the empirical values of the nuclear matter saturation density, binding energy, and nuclear incompressibility. The value of the incompressibility is chosen according to recently obtained heavy-ion collision data. We then apply the same dynamical model to neutronrich matter in beta equilibrium, related to neutron star structure. The maximum mass and corresponding radius of stable non-rotating neutron stars are found to be in the observational limit.
TL;DR: In this article, an exterior electromagnetic field surrounding a rotating star endowed with a dipole magnetic field was considered in the context of general relativity, and the general relativistic modifications and the implications for pulsar radiation were investigated in detail.
Abstract: We consider an exterior electromagnetic field surrounding a rotating star endowed with a dipole magnetic field in the context of general relativity. The analytic solution for a stationary configuration is obtained, and the general relativistic modifications and the implications for pulsar radiation are investigated in detail. We find that the general relativistic corrections of both the electric field strength and the curvature radii of magnetic field lines tend to enhance the curvature radiation photon energy.
TL;DR: In this article, the scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives, and it is shown that the R 2 sector of the theory does not contribute to the photon scattering, whereas the R 3 sector produces dispersive (energy-dependent) photon propagation.
Abstract: The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R 2 sector of the theory does not contribute to the photon scattering, whereas the R 2 sector produces dispersive (energy-dependent) photon propagation.
TL;DR: In this paper, the Kramers-Wannier approximation for the 3D Ising model was investigated and the variational partition function was numerically calculated using the corner transfer matrix renormalization group (CTMRG) method.
Abstract: We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational parameters. The value of the calculated transition point, Kc = 0.2184, is only 1.5% less than the true Kc. This result is better than that obtained using the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-field like.
TL;DR: In this article, the angular-diameter distance is calculated by integrating the Raychaudhuri equation including the shear, and an explicit expression for the junction condition for the massive thin shell is calculated.
Abstract: Propagation of light in a clumpy universe is examined. As an inhomogeneous matter distribution, we take a spherical void surrounded by a dust shell, where the “lost mass” in the void is compensated by the shell. We study how the angular-diameter distance behaves when such a structure exists. The angular-diameter distance is calculated by integrating the Raychaudhuri equation including the shear. An explicit expression for the junction condition for the massive thin shell is calculated. We apply these results to a dust shell embedded in a Friedmann universe and determine how the distance-redshift relation is modified compared with that in the purely Friedmann universe. We also study the distribution of distances in a universe filled with voids. We show that the void-filled universe gives a larger distance than the FRW universe by ∼ 5% at z ∼ 1 if the size of the void is ∼ 5% of the Horizon radius.
TL;DR: In this article, a non-Abelian Stokes theorem for general semi-simple compact groups is presented, which involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops.
Abstract: A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the ’t Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the case of the fundamental representation of the group SU(N) is pointed out.
TL;DR: In this article, the absorption rate of the Kerr-de-Sitter and the KerrNewman-de Sitter black holes was derived by using the analytic solution of the Teukolsky equation.
Abstract: In a series of papers, 1), 2) we have developed a method to obtain an analytic solution of the Teukolsky equation 3) in Kerr geometries, the perturbation equation of massless particles in Kerr geometries. This method is applied to evaluate the gravitational wave from a binary of neutron stars. 4) Recently, we extended this method to Kerr-de Sitter and Kerr-Newman-de Sitter geometries and showed that an analytic solution can be similarly obtained. 5) It has been shown that the analytic solution obtained in Ref. 5) can be analytically continued to cover the entire physical region. 6) It should be noted that in Kerr-Newman-de Sitter geometries, electromagnetic and gravitational perturbations couple to each other, and thus these particles are excluded. In this paper, we evaluate the absorption rate of the Kerr-de Sitter and the Kerr-Newman-de Sitter black holes by using the analytic solution. We construct the conserved current by evaluating the Wronskian, and we obtain an expression of the absorption rate. From this, we show explicitly that super-radiance occurs for the boson case similarly to the Kerr geometry case. 2) The paper is organized as follows. In §2 we summarize the construction of analytic solutions in order to define parameters involved in them. In §3 we choose the solution which satisfies the incoming boundary conditions at the outer horizon of the black hole and examine the asymptotic behavior at the de Sitter horizon. Then, we derive analytic expressions of the incident, the reflection and the transmission amplitudes. In §4 we derive the conserved current, from which we derive the absorption rate. A summary is given in §5.