Flavour and spin structure of linear baryons

Based on the string picture, we construct a phenomenological model for baryons and study their flavour symmetry, exchange degeneracy pattern and spin structure. Baryons on leading trajectories are assumed to have the configuration of two quarks being attached to the ends of a linear string and the third sitting in the middle, called linear baryons. For such linear baryons, a unitarization scheme can be constructed in a manner similar to the dual unitarity scheme for mesons but without recourse to the $\text{1}\text{N}$ expansion. We find that the interchange interaction of the middle quark with one of the other two quarks at the ends of the string can give rise to a large exchange degeneracy breaking of the baryon spectrum. With this non-planar correction, the model of linear baryons can account for the observed pattern of leading baryon states.     

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.     

Two mass relations for mesons from string-quark duality

We generalize a self-consistency equation derived previously by us for the Nambu string to strings carrying SU(6) quantum numbers.The self-consistency equations are derived by considering the propagation of a string with the quantum numbers of the physical vacuum. Since we can map the world sheet that the string sweeps out onto rectangles, and the wave function of the physical vacuum is a constant, the boundary conditions are the same on all four sides of the rectangles. We can then calculate the propagator in two ways and this leads to the self-consistency equations. For the strings carrying SU(6) quantum numbers we consider the propagator o strings with the quantum numbers of the physical vacuum all along the string except for having quark quantum numbers either attached or removed from the ends. We can solve these self-consistency equations in a certain approximation and for this case they lead to mass formulae for mesons that are well satisfied in nature.     

Quarks and diquarks in a baryon string model

Chew-Frautschi plots are found for baryons containing a quark and a diquark at the extremities of a relativistic string. The quark fields are modelled on free Dirac fields restricted to the ends of the string. Quantum numbers for the diquark field are obtained by adding those for two individual quark fields.The leading trajectory for the quark-diquark configuration is found to be energetically more favourable than the leading trajectories for the linear and Y-shaped baryon configurations considered previously.     

On a Class of World Surfaces for the Linear String Model of a Baryon

For the linear string model of a baryon where three material points (three quarks) are connected in series by relativistic strings, a class of physically realizable world surfaces has been found which admit parametrization such that the equations of motion and the boundary conditions are linear due to the proportionality of the parameter associated with the quark trajectories to the natural parameter. The surfaces of this class are represented as a Fourier series of the eigenfunctions of some boundary-value problem. It is shown that the series generating such surfaces contains a finite number of terms. In particular, in the 3+1-dimensional Minkowski space, one and only one surface of the class under consideration is realizable, namely, the helicoid.     

Stationary properties of Nambu strings

It is shown that the string equations and boundary conditions for the open massless string do not follow consistently from the Nambu action. Nevertheless, all solutions are stationary under those variations which result in time-like or null surfaces. For strings with masses attached to the ends no consistency problems arise.     

Decoherence and CPT Violation in a Stringy Model of Space-Time Foam

I discuss a model inspired from the string/brane framework, in which our Universe is represented (after perhaps appropriate compactification) as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a “space-time foam” with the defects “flashing” on and off (“D-particle foam”). The open strings, with their ends attached on the brane, which represent matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manner, involving splitting and capture of the strings by the D0-brane defects. Such processes are consistently described by logarithmic conformal field theories on the world-sheet of the strings. Physically, they result in effective decoherence of the string matter on the D3 brane, and as a result, of CPT Violation, but of a type that implies an ill-defined nature of the effective CPT operator. Due to electric charge conservation, only electrically neutral (string) matter can exhibit such interactions with the D-particle foam. This may have unique, experimentally detectable (in principle), consequences for electrically-neutral entangled quantum matter states on the brane world, in particular the modification of the pertinent Einstein-Podolsky-Rosen (EPR) Correlation in neutral mesons in an appropriate meson factory. For the simplest scenarios, the order of magnitude of such effects might lie within the sensitivity of upgraded φ-meson factories.     

Test particle trajectories near cosmic strings

We present a detailed analysis of the motion of test particle in the gravitational field of cosmic strings in different situations using the Hamilton-Jacobi (H-J) formalism. We have discussed the trajectories near static cosmic string, cosmic string in Brans-Dicke theory and cosmic string in dilaton gravity.     

Some solutions of the equations of motion of the relativistic string with massive ends

The classical theory is discussed for the relativistic string with point masses at its ends. The dynamical equations are solved for the class of motions of this system when the time evolution parameter τ is the proper time of both massive string ends. In this case the solution of the boundary equations is given by the almost periodic functions. Constraints on the normal modes resulting from the orthonormal gauge conditions differ essentially from the Virasoro ones. Incidentally one obtains an exact solution for the half-infinite string with mass at one end. It is also proved that the exact solution for the string with massive ends cannot be a periodic function.     

Disturbances of Rotational Motions for String Models of Hadrons and the Stability Problem

Slight disturbances of a classical rotational motion (uniform rotation of a system) are considered for a relativistic string with massive ends and for the q-q-q and Y baryon string models. It is shown that for a string with massive ends this motion is stable in the linear approximation and the slight perturbations are representable by a series each term of which describes a standing wave of certain frequency. These modes make it possible to simulate various excited states of hadrons. At the same time, for the q-q-q and Y baryon string models the instability of rotational motions has been proved: exponentially growing modes have been detected in their perturbation spectra.     

Classical symmetries of some two-dimensional models

It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, supersymmetrization, and quantum effects. However, as a first step, this paper only considers classical bosonic theories in flat space-time. Even though the algebra of hidden symmetries of principal chiral models is confirmed to include a Kac-Moody algebra (or a current algebra on a circle), it is argued that a better interpretation is provided by a doubled current algebra on a semi-circle (or line segment). Neither the circle nor the semi-circle bears any apparent relationship to the physical space. For symmetric space models the line segment viewpoint is shown to be essential, and special boundary conditions need to be imposed at the ends. The algebra of hidden symmetries also includes Virasoro-like generators. For both principal chiral models and symmetric space models, the hidden symmetry stress tensor is singular at the ends of the line segment.     

Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking

A study of ray trajectories was undertaken for the Tamm medium which represents the spacetime of a zero-tension cosmic spinning string, under the geometric-optics approximation. Our numerical studies revealed that: (i) rays never cross the string's boundary; (ii) the Tamm medium supports evanescent waves in regions of phase space that correspond to those regions of the string's spacetime which could support closed timelike curves; and (iii) a spinning string can be slightly visible while a non-spinning string is almost perfectly invisible.     

A two-dimensional superfield formulation of the heterotic string

The density superfield and Einstein action for two-dimensional (2,0) supergravity are derived. The irreducible superfields of the heterotic string are discussed, and they are coupled to (2,0) supergravity. The locally (2,0) supersymmetric action for the heterotic string is presented in both superfields and component fields. For flat world sheet geometry, the globally (2,0) supersymmetric non-linear sigma model, and the associated Virasoro constraints, are derived. This formalism is applicable to (p,0) supersymmetry for any positive integer p.     

The Casimir energy of the rigid string with massive ends

The Casimir energy in the rigid string with massive ends is investigated. This system models the flux tube of finite thickness that connects the massive quarks. The string stiffness and quark mass give additive contributions to the Casimir energy, the second contribution being the same as in the Nambu-Goto string with massive ends. The string stiffness results in an additional positive contribution to the Casimir energy, however it alone does not compensate the negative Casimir energy in the Nambu-Goto string. Only common consideration of the string thickness and the quark mass enables one to get the positive Casimir energy, i.e. to remove the tachyon from the string spectrum.     

Classical dynamics of the rigid string from the Willmore functional

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into a space of constant curvature. It is shown that the rigid string in flat space-time is described by the Euler-Lagrange equation for the Willmore functional in a space-time of constant curvature K = −γ/(2α), where γ and α are constants in front of the Nambu-Goto term and the curvature term in the rigid string action, respectively. For simplicity the Euclidean version of the rigid string in three-dimensional space-time is considered. The Willmore functional (the action for the “Willmore string”) is obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for the rigid string. Such a “reduction” of the rigid string model would be useful, for example, by applying some results about the Nambu-Goto string dynamics in the de Sitter universe to the rigid string model in the Minkowski space-time. It also allows us to use numerous mathematical results about Willmore surfaces in the context of the physical problem.     

The conformal killing anomaly of the Polyakov string

For world sheets with the topology of the disc or sphere, part of the gauge group for the Polyakov string is broken by any regulator, namely the group of conformal isometries×Weyl rescalings which leave the metric unchanged. there exist no local counterterms that can restore the symmetry. This implies that the factor of 1/(volume of conformal isometries) in the computation of string amplitudes is not equivalent to fixing this gauge symmetry, but rather corresponds to averaging over inequivalent gauges.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Relativistic string model of light mesons with massless quarks

The straightline string model of mesons with massless fermions (“quarks”) at the string endpoints is constructed. The spectrum of the model, consisting of four Regge trajectories weakly non-linear atM ²～0, is obtained. A comparison of the model predictions with the experimental spectrum of light mesons and prospects for future searches are discussed.     

String dynamics near a black hole

The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the geodesic equations are obtained using the world sheet velocity of light as an expansion parameter. For a string falling into a magnetically charged black hole, it is shown that the compact dimension decreases with the world-sheet coordinate τ.     

Path integral over reparametrizations: Lévy flights versus random walks

We investigate the properties of the path integral over reparametrizations (or the boundary value of the Liouville field in string theory). Discretizing the path integral, we apply the Metropolis–Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Lévy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby previous results on QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.