Relativistic String Research Articles

CLASSICAL SOLUTIONS OF SIGMA MODELS IN CURVED BACKGROUNDS BY THE POISSON–LIE T-PLURALITY

Classical equations of motion for three-dimensional σ-models in curved background are solved by a transformation that follows from the Poisson–Lie T-plurality and transform them into the equations in the flat background. Transformations of coordinates that make the metric constant are found and used for solving the flat model. The Poisson–Lie transformation is explicitly performed by solving the PDE's for auxiliary functions and finding the relevant transformation of coordinates in the Drinfel'd double. String conditions for the solutions are preserved by the Poisson–Lie transformations. Therefore we are able to specify the type of σ-model solutions that solve also equations of motion of three-dimensional relativistic strings in the curved backgrounds. Some simple examples are given.

Regularities in hadron systematics, Regge trajectories and a string quark model

An empirical principle for the construction of a linear relationship between the total angular momentum and squared-mass of baryons is proposed. In order to examine linearity of the trajectories, a rigorous least-squares regression analysis was performed. Unlike the standard Regge-Chew-Frautschi approach, the constructed trajectories do not have non-linear behaviour. A similar regularity may exist for lowest-mass mesons. The linear baryonic trajectories are well described by a semi-classical picture based on a spinning relativistic string with tension. The obtained numerical solution of this model was used to extract the (di)quark masses.

UCLA space-time area law model: A persuasive foundation for hadronization

From the studies of rates and distributions of heavy quark (c, b) mesons we have developed additional evidence that hadron formation, at least in the simplest environment of e+e- collisions, is dominantly controlled by a space-time area law (“STAL”), an approach suggested by both non-perturbative QCD and relativistic string models. From the dynamics of heavy quarks whose classical space-time world-lines deviate significantly from the light-cone, we report the exact calculation of the relevant space-time area and the derivation of a Lorentz invariant variable, zeff, which reduces to the light-cone momentum fraction z for low mass quarks. Using zeff in the exponent of our fragmentation function in place of z, we find persuasive agreement with L=0, 1 charmed and bottom meson data as well as for u, d, s L=0 states. Presuming STAL to be a valid first-order description for all these meson data, we find the scale of other possible second-order effects to be limited to ∼20% or less of the observed rates. The model favors a b-quark mass of ∼4.5 GeV.

The Dynamics of Relativistic Strings Moving in the Minkowski Space $$\mathbb{R}^{1+n}$$

In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space \(\mathbb{R}^{1+n}\;(n\ge 2)\). We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in \(\mathbb{R}^{1+n}\). We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in \(\mathbb{R}^{1+n}\) with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in \(\mathbb{R}^{1+n}\). We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in \(\mathbb{R}^{1+n}\) are given.

SU(Nc→∞)lattice data and degrees of freedom of the QCD string

Lattice simulation data on the critical temperature and long-distance potential, that probe the degrees of freedom of the QCD string, are critically reviewed. It is emphasized that comparison of experimental or SU(N_c) lattice data, at finite number of colors N_c, with free string theory can be misleading due to string interactions. Large-N_c extrapolation of pure lattice gauge theory data, in both 3 and 4 dimensions, indicates that there are more worldsheet degrees of freedom than the purely massless transverse ones of the free Nambu-Goto string. The extra variables are consistent with massive modes of oscillation that effectively contribute like c ~ 1/2 conformal degrees of freedom to highly excited states. As a concrete example, the highly excited spectrum of the Chodos-Thorn relativistic string in 1+1 dimensions is analyzed, where there are no transverse oscillations. It is found that the asymptotic density of states for this model is characteristic of a c=1/2 conformal worldsheet theory. The observations made here should also constrain the backgrounds of holographic string models for QCD.

Can one ADM quantize relativistic bosonicstrings and membranes?

The standard methods for quantizing relativistic strings diverge significantly from the Dirac-Wheeler-DeWitt program for quantization of generally covariant systems and one wonders whether the latter could be successfully implemented as an alternative to the former. As a first step in this direction, we consider the possibility of quantizing strings (and also relativistic membranes) via a partially gauge-fixed ADM (Arnowitt, Deser and Misner) formulation of the reduced field equations for these systems. By exploiting some (Euclidean signature) Hamilton-Jacobi techniques that Mike Ryan and I had developed previously for the quantization of Bianchi IX cosmological models, I show how to construct Diff(S 1)-invariant (or Diff(Σ)-invariant in the case of membranes) ground state wave functionals for the cases of co-dimension one strings and membranes embedded in Minkowski spacetime. I also show that the reduced Hamiltonian density operators for these systems weakly commute when applied to physical (i.e. Diff(S 1) or Diff(Σ)-invariant) states. While many open questions remain, these preliminary results seem to encourage further research along the same lines.

Cosmic string lensing and closed timelike curves

In an analysis of the gravitational lensing by two relativistic cosmic strings, we argue that the formation of closed time-like curves proposed by Gott is unstable in the presence of particles (e.g. the cosmic microwave background radiation). Due to the attractor-like behavior of the closed time-like curve, we argue that this instability is very generic. A single graviton or photon in the vicinity, no matter how soft, is sufficient to bend the strings and prevent the formation of closed time-like curves. We also show that the gravitational lensing due to a moving cosmic string is enhanced by its motion, not suppressed.

String behaviour of magnetic field lines and their rotation in neutron star’s interior

It is found from Maxwell’s equations that the magnetic field lines are good analogues of relativistic strings. The Lorentz force per unit length of magnetic tube is interpretable as Magnus force acting on each individual magnetic tube. It is shown that the superconducting current in pulsar’s interior causes local rotation of magnetic flux tubes carrying quantized flux. Such local rotation remains operative as long as the induced magnetic field of normal electron fluid is above the lower critical field but below the upper. The conservation of magnetic flux leads to a geometrical condition in the form of the Weingarten identity which ensures the existence of family of “magnetic world sheetrdquo;. Each “magnetic world sheet” is a magnetic flux conserving surface. In the process of collapse, a compact spacelike cross-section of a magnetic tube terminates into a trapped surface if the magnetic energy grows faster along the fluid flow lines than that along the magnetic field lines.

How to lasso a plane gravitational wave

Beginning with the stress-energy tensor of an elastic string this paper derives a relativistic string and its form in a parallel transported Fermi frame including its reduction in the Newtonian limit to a Cosserat string. In a Fermi frame gravitational curvature is seen to induce three dominant relative acceleration terms dependent on: position, velocity and position, strain and position, respectively. An example of a string arranged in an axially flowing ring (a lasso) is shown to have a set of natural frequencies that can be parametrically excited by a monochromatic plane gravitational wave. The lasso also exhibits, in common with spinning particles, oscillation about geodesic motion in proportion to spin magnitude and wave amplitude when the spin axis lies in the gravitational wave front. Coordinate free notation is used throughout including the development of the properties of the Fermi frame.

The description of pairs of compatible first-order differential geometric poisson brackets

We find exact solutions of the equations of motion for a closed relativistic string that carries a point mass and moves in the space given by the direct product of Minkowski space and a compact manifold (multidimensional torus). We investigate physical characteristics of the system states described by these solutions.

Non Relativistic Strings may be Approximated by Relativistic Strings

We show that bounded families of global classical relativistic strings that can be written as graphs are relatively compact in C0 topology, but their accumulation points include many non relativistic strings. We also provide an alternative formulation of these relativistic strings and characterize their ``semi-relativistic'' completion.

Closed relativistic strings in geometrically nontrivial spaces

Closed relativistic strings in geometrically nontrivial spaces

Functionals linear in curvature and statistics of helical proteins

It is shown that proceeding from the spiral stationary form of the protein chains one can deduce, in a unique way, the explicit expression for the relevant free energy. Namely, the free energy density should be a linear function of the curvature k of the curve which describes the shape of the central line of the protein molecule. Minimization of this energy gives for the pitch-to-radius ratio of the helices the value 2 π. The model also enables one to estimate qualitatively the release of the free energy under the transition of the protein chain from the straight line form to the spiral form. The free energy we propose implies, in particular, that the effective bending energy of the protein chain is not proportional to k 2 , as it is usually adopted in the physics of semi-flexible polymers, but this energy is linear in the curvature k. The relation of this model to the rigid relativistic particles and strings is briefly discussed. The consideration relies on proving the complete integrability of the variational equations for the functionals defined on smooth curves and dependent on the curvature of these curves.

Perturbed States of a Rotating Relativistic String

We investigate arbitrary small perturbations of the uniform rotation of a rectilinear relativistic string with massive ends. Two classes of such perturbations with different spectra of eigenfrequencies have the form of stationary waves and correspond to string oscillations in the rotation plane and in the orthogonal direction. These states are represented by the Fourier series used to quantize string excitations in the linear neighborhood of the classical rotation. These string oscillations can be used to describe daughter Regge trajectories in the framework of the considered model.

The pole heavy-quark masses in the Hamiltonian approach

From the fact that nonperturbative self-energy contribution C SE to the heavy-meson mass is small, $$C_{SE} (b\bar b) = 0$$ and $$C_{SE} (c\bar c) \cong - 40$$ MeV, strong restrictions on the pole masses m b and m c are obtained. The analysis of the $$b\bar b$$ and the $$c\bar c$$ spectra with the use of the relativistic (string) Hamiltonian gives m b(2-loop)=4.78±0.05 GeV and m c(2-loop)=1.39±0.06 GeV, which correspond to the $$\overline {MS} $$ running masses $$\bar m_b (\bar m_b ) = 4.19 \pm 0.04$$ GeV and $$\bar m_c (\bar m_c ) = 1.14 \pm 0.05$$ GeV.

Letter: Behavior of Magnetic Tubes in Neutron Star's Interior

It is found from Maxwell's equations that the magnetic field lines are good analogues of relativistic strings. It is shown that the super-conducting current in the neutron star's interior causes local rotation of magnetic flux tubes carrying quantized flux.

Relativistic string in a pulse

I study a relativistic open string coupling through its endpoints to a plane wave with arbitrary temporal profile. The string’s transverse oscillations respond linearly to the external field. This makes it possible to solve the classical equations, and to calculate the quantum-mechanical S-matrix in closed form. I analyze the dynamics of the string as the characteristic frequency and duration of the pulse are continuously varied. I derive, in particular, the multipole expansion in the adiabatic limit of very long wavelengths, and discuss also more violent phenomena such as shock waves, cusps, and null brane intersections. Apart from their relevance to the study of time-dependence in superstring theory, these results could have other applications, such as the teleportation of gravitational wave bursts by cosmic strings.

Chiral superconducting strings and Nambu–Goto strings in arbitrary dimensions

We present general solutions to the equations of motion for a superconducting relativistic chiral string that satisfy the unit magnitude constraint in terms of products of rotations. From this result we show how to construct a general family of odd harmonic superconducting chiral loops. We further generalize the product of rotations to an arbitrary number of dimensions.

Instability of the Y string baryon model within classical dynamics

For the three-string baryon model (Y configuration), the known exact solution to the classical equations of motion that describes the rotational motion of the system at a constant speed is investigated for stability. In the spectrum of small perturbations of this solution, modes growing exponentially with time are found, whereby the instability of rotational motion is proven for the Y configuration. This result is confirmed within an alternative approach that makes it possible to determine the classical motion of the system from a specific initial position and initial velocities of string points. A comparison of the Y configuration with the model of a relativistic string with massive ends, in which case rotational motion is stable in the linear approximation, aids in revealing the most adequate string model from the point of view of describing baryon excitations on Regge trajectories.

Lund–Regge vortex strings in terms of Weierstrass elliptic functions

We study quasi-periodic solutions of the Lund–Regge model in terms of the elliptic functions of Weierstrass. They describe the Kida-class motions of relativistic strings in an external antisymmetric tensor field. Our solution includes various vortex string shapes such as the closed vortex ring, the helicoidal filament, the generalized Zee's solution and the Hasimoto type 1-soliton filament.