Existence of dual mass: Experimental evidence

This second article on dual mass investigates the physical evidence for the existence of dual mass. We discuss three possible observations that could be used to bound the amount of dual mass in the solar system: the Eotvos experiment, the relativistic pendulum, and planetary orbits. The Eotvos experiment is used to conclude that the ratio of dual mass to ordinary mass is a constant. Under this assumption the dual mass effects are proportional to a dimensionless parameter which is proportional to the ratio of dual to ordinary mass. We consider two effects: First we show that a pendulum swinging in the gravitational field of the earth would be subject to a precession of the plane of oscillation; second, we show that dual mass in the solar system creates a lifting of planetary orbits. Observations of a pendulum should yield to an accuracy of 10^–4 and limits on the detectability of the planetary lifting puts an upper bound on of about 10^–1.     

Supersymmetrical dual string theory

It is proved that the physical states of the open-string sector of the ten-dimensional string theory form supersymmetry multiplets. The proof is achieved by first constructing a new formulation of the spectrum generating algebra, and then forming the supersymmetry operator (as well as associated operators) and demonstrating that it transforms as a spinor under Lorentz transformations and has the correct anticommutation relations. The results can be interpreted either in terms of a covariant formulation or in terms of a light-cone gauge formulation. In the former case certain formulas are not completely proved, although they are in the latter. When interpreted in four dimensions (by dimensional reduction) the string theory provides an interacting theory of an infinite number of massive representations of N = 4 supersymmetry involving particles of arbitrarily high spin.     

A theory of dual massive strings

A theory of relativistic strings with non-vanishing mechanical mass is developed. The theory involves the usual massless strings, and the main features of the massless theory are retained so that the system is dual and ghost-free. Some new features appear especially in the mass spectrum of the pomeron sector. The mode with Neveu-Schwarz spin is also considered.     

Linear dilaton conformal field theory: a generalization

We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable us to study a more general case. Various properties of the model such as OPEs, central charge, conformal properties of the fields and associated algebras will be studied.     

Off-shell states in dual resonance theory

We discuss ooff-shell states guided by an analogue model approach. This leads us to a more complete understanding of a model proposed recently by Schwarz with critical dimension 16. We are led, by algebraic considerations, to off-shell states in the Neveu- Schwarz-Ramond model, which obey the gauge conditions in the same critical dimension as the on-shell theory, the amplitudes factorizing on the usual positive definite states in 10 dimensions. Brief calculations reveal that some of the divergences present in the orbital model disappear in the fermion theory.     

Gauge identities in dual field theory

In the dual and fermion proposed by Neveu, Schwarz and Ramond, we find gauge identities involving vertex parts and also off-shell supergauge identities. When their models are translated into the secondary quantized field theory, we no longer can impose the gauge identities as operator ones, since they would lead to a contradiction of the second-quantization rules. We therefore require weak forms of the gauge identities just in an analogous way to the Lorentz condition in quantum electrodynamics. It is then shown that the weak forms of the identities are consistent with the second-quantization rules and also with field equations.     

Linear response theory in nuclei

A new method is proposed for the treatment of a perturbing field as well as the perturbation due to the addition of a particle. The variational equations obtained from a Thouless-type trial function are linearized. The higher order equations are similar to the first order equations, only the inhomogenous terms are different. These equations have been derived for the Hartree-Fock-Bogolyubov (HFB) ground state of the N-particle system. An application of the method to the exactly soluble Lipkin model is also presented. The proposed method meets a high degree of success in the model case. We further argue that the present method is superior to the blocked HFB method and also numerically simpler, for the addition of a particle.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

Existence of solutions for a generalized Yang-Mills theory

The main result of this note is a proof of a conjecture of Burzlaff, O'Sé and Tchrakian [1] concerning the existence of a certain kind of finite action solutions of the seven-dimensional generalized Yang-Mills-Higgs model derived from an eight-dimensional SO(8) Yang-Mills theory.     

Existence of dual solutions and three-dimensional instability in helical pipe flow

Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.     

Intermediate mass distribution of the dual resonance pomeron

We determine the intermediate mass distribution of the dual resonance pomeron at the one-loop level and we show that the mass distribution obtained is remarkably similar to a suitably defined mass distribution in the dual multiperipheral model. Thus it is suggestive to identify the intermediate states of the dual resonance pomeron with multipheripheral processes.     

Supersymmetric dual string theory: (III). Loops and renormalization

The mixing of 0^?+ glueballs (G) and ordinary ¯qq mesons is calculated in the MIT bag model. The result is that the η and η′ have probabilities 7% and 19%, respectively, of being pure glue-glue state. This has implications for the η-η′ mass difference, and allows a quantitative estimate of the widths for G(0^?+)→γγ and γp, which may help distinguish a glueball from ¯qq mesons.     

Supersymmetric dual string theory: (II). Vertices and trees

Vertex operators for the emission of massless open-string states are constructed using the light-cone gauge formalism introduced in the first paper of this series. The vertices for vector and spinor emission transform into one another under supersymmetry in the same way as the states themselves. This enables one to construct amplitudes and deduce the relationships among them implied by supersymmetry. Various four-particle tree graphs are explicitly investigated and shown to satisfy the duality requirement.     

Holographic dual of a boundary conformal field theory

We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our new holography, which may be called anti-de?Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.     

Polaron cyclotron mass: Validity of second-order perturbation theory

The cyclotron mass of three-dimensional polarons is studied within different approximations. The validity of different perturbation theories is critically examined as a function of the magnetic field and the electron-phonon coupling strength. The importance of non-perturbative effects is pointed out.