Splitting Of Strings Research Articles

The decay width of stringy hadrons

In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as Γ=π2ATL where T and L are the tension and length of the string and A is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by Γi/Γ=Φiexp⁡(−2πCmsep2/T) where Φi is a phase space factor, msep is the mass of the “quark” and “antiquark” created at the splitting point, and C is a dimensionless coefficient close to unity. Based on the spectra of hadrons we observe that their (modified) Regge trajectories are characterized by a negative intercept. This implies a repulsive Casimir force that gives the string a “zero point length”.We fit the theoretical decay width to experimental data for mesons on the trajectories of ρ, ω, π, η, K⁎, ϕ, D, and Ds⁎, and of the baryons N, Δ, Λ, and Σ. We examine both the linearity in L and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons A=0.095±0.015 is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. We discuss the relation with string fragmentation and jet formation. We extract the quark–diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia is proposed and is shown to reproduce the decay width of ϒ states. The dependence of the width on spin and flavor symmetry is discussed. We further apply this model to the decays of glueballs and exotic hadrons.

High Efficient Consistency Maintenance Strategy of Real-time String Text Editing Systems

The idea of address space transformation provides a new way for concurrency control. During concurrent processing, it retraces the document status back to the state when the operations are generated to maintain consistency. However the previous concurrency processes strategy is based on single characters, the transmission cost during processing is too high, especially when the network is unstable. Due to this problem, this paper presents a consistency maintenance strategy based on string editing operations, and proposes the string splitting mechanism combined with the idea of the address space transformation in order to maintain consistency.

Splitting of folded strings inAdS3

In this paper we present semiclassical computations of the splitting of folded spinning strings in ${\mathrm{AdS}}_{3}$, which may be of interest in the context of AdS/CFT duality. We start with a classical closed string and assume that it can split into two closed string fragments, if at a given time two points on it coincide in target space and their velocities agree. First we consider the case of the folded string with large spin. Assuming the formal large-spin approximation of the folded string solution in ${\mathrm{AdS}}_{3}$, we can completely describe the process of splitting: compute the full set of charges and obtain the string solutions describing the evolution of the final states. We find that, in this limit, the world surface does not change in the process and the final states are described by the solutions of the same type as the initial string, i.e. the formal large-spin approximation of the folded string in ${\mathrm{AdS}}_{3}$. Then we consider the general case---splitting of string given by the exact folded string solution. We find the expressions for the charges of the final fragments, the coordinate transformations diagonalizing them and, finally, their energies and spins. Because of the complexity of the initial string profile, we cannot find the solutions describing the evolution of the final fragments, but we can predict their qualitative behavior. We also generalize the results to include circular rotations and windings in ${\mathrm{S}}^{5}$.

Boson-Fermion Unification, Superstrings, and Bohmian Mechanics

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.

Quasilocality of joining/splitting strings from coherent states

Using the coherent state formalism we calculate matrix elements of the one-loop non-planar dilatation operator of = 4 SYM between operators dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior. We comment on the qualitative similarity of our matrix elements to the interaction vertex of a string field theory. In addition, we present a solvable toy model for string splitting and joining. The scaling behaviour of the matrix elements suggests that the contribution to the genus one energy shift coming from semi-classical string splitting and joining is small.

String Splitting and Strong Coupling Meson Decay

We study the decay of high spin mesons using the gauge-string theory correspondence. The rate of the process is calculated by studying the splitting of a macroscopic string intersecting a D-brane. The result is applied to the decay of mesons in N=4 super Yang-Mills theory with a small number of flavors and in a gravity dual of large N QCD. In QCD the decay of high spin mesons is found to be heavily suppressed in the regime of validity of the supergravity description.

The acoustics of hammered dulcimers

The hammered dulcimer, a stringed instrument played with two wooden hammers, probably originated in the Middle East, but it has become part of the musical culture of many countries. In the U. S., the folk revivial in the 1970’s sparked renewed interest in the hammered dulcimer as a concert instrument. Today, despite some consolidation in the retail market, there are still hundreds of builders, mostly amateurs, who experiment with the basic design. The most important design parameters will be discussed from a practical and acoustical point of view: soundboard size, shape, and composition, internal bracing, bridge shape, string arrangement and composition, hardness of bridge caps, hammer weight and stiffness, instrument resonances due to the unique string splitting and stiffness of the body, and soundboard modes.

Magnetic fields, branes, and noncommutative geometry

We construct a simple physical model of a particle moving on the infinite noncommutative 2-plane. The model consists of a pair of opposite charges moving in a strong magnetic field. In addition, the charges are connected by a spring. In the limit of large magnetic field, the charges are frozen into the lowest Landau levels. Interactions of such particles include Moyal-bracket phases characteristic of field theories on noncommutative space. The simple system arises in the light cone quantization of open strings attached to D-branes in antisymmetric tensor backgrounds. We use the model to work out the general form of light cone vertices from string splitting. We then consider the form of Feynman diagrams in (uncompactified) noncommutative Yang-Mills theories. We find that for all planar diagrams the commutative and noncommutative theories are exactly the same apart from trivial external line factors. This means that the large N theories are equivalent in the 't Hooft limit. Non-planar diagrams are generally more convergent than their commutative counterparts.

Classical splitting of fundamental strings.

We find exact solutions of the string equations of motion and constraints describing the {\em classical}\ splitting of a string into two. We show that for the same Cauchy data, the strings that split have {\bf smaller} action than the string without splitting. This phenomenon is already present in flat space-time. The mass, energy and momentum carried out by the strings are computed. We show that the splitting solution describes a natural decay process of one string of mass $M$ into two strings with a smaller total mass and some kinetic energy. The standard non-splitting solution is contained as a particular case. We also describe the splitting of a closed string in the background of a singular gravitational plane wave, and show how the presence of the strong gravitational field increases (and amplifies by an overall factor) the negative difference between the action of the splitting and non-splitting solutions.

Back reaction of strings in self-consistent string cosmology

We compute the string energy-momentum tensor and {\bf derive} the string equation of state from exact string dynamics in cosmological spacetimes. $1+1,~2+1$ and $D$-dimensional universes are treated for any expansion factor $R$. Strings obey the perfect fluid relation $ p = (\gamma -1) \rho $ with three different behaviours: (i) {\it Unstable} for $ R \to \infty $ with growing energy density $ \rho \sim R^{2-D} $, {\bf negative} pressure, and $ \gamma =(D-2)/(D-1) $; (ii){\it Dual} for $ R \to 0 $, with $ \rho \sim R^{-D} $, {\bf positive} pressure and $\gamma = D/(D-1) $ (as radiation); (iii) {\it Stable} for $ R \to \infty $ with $ \rho \sim R^{1-D} $, {\bf vanishing} pressure and $\gamma = 1 $ (as cold matter). We find the back reaction effect of these strings on the spacetime and we take into account the quantum string decay through string splitting. This is achieved by considering {\bf self-consistently} the strings as matter sources for the Einstein equations, as well as for the complete effective string equations. String splitting exponentially suppress the density of unstable strings for large $R$. The self-consistent solution to the Einstein equations for string dominated universes exhibits the realistic matter dominated behaviour $ R \sim (X^0)^{2/(D-1)}\; $ for large times and the radiation dominated behaviour $ R \sim (X^0)^{2/D}\; $ for early times. De Sitter universe does not emerge as solution of the effective string equations. The effective string action (whatever be the dilaton, its potential and the central charge term) is not the appropriate framework in which to address the question of string driven inflation.

Quantum string scattering in a cosmic-string space-time.

We exactly quantize fundamental strings propagating in a straight cosmic-string space-time (conical space-time with deficit angle $8\ensuremath{\pi}G\ensuremath{\mu}$, $\ensuremath{\mu}$ being the cosmic-string tension). If the fundamental string collides with the cosmic string the scattering is inelastic since the internal modes of the fundamental string become excited. If there is no collision, the fundamental string only suffers a deflection of $\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}G\ensuremath{\mu}$. If there is collision we find inelastic particle production from the interaction of the string with the (classical) geometry. The string oscillator modes only suffer a change of polarization (rotation) in the elastic case and a Bogoliubov transformation in the inelastic case. As a consequence, for a given initial state, the final particle may be in any state associated with the string oscillators. All transformations are explicitly calculated in closed form. Finally, the quantum scattering amplitude for the lowest scalar (tachyon) is computed exactly. In this calculation the vertex operator in the conical geometry and the oscillator linear transformations we find here are used thoroughly. The peculiar features of the string propagation in this topologically nontrivial space-time are discussed including the question whether string splitting can occur at the classical level.

Dyson-Schwinger equations approach to the large-Nlimit: Model systems and string representation of Yang-Mills theory

Simple model systems like the $\mathrm{O}(N)$ $\ensuremath{\sigma}$ model, the Gross-Neveu model, and the random matrix model are solved at $N\ensuremath{\rightarrow}\ensuremath{\infty}$ using Dyson-Schwinger equations and the fact that the Hartree-Fock approximation is exact at $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The complete string equations of the $U(\ensuremath{\infty})$ lattice gauge theory are presented. These must include both string rearrangement and splitting. Comparison is made with the continuum equations of Makeenko and Migdal which are structurally different. The difference is ascribed to inequivalent regularization procedures in the treatment of string splitting or rearrangement at intersections.

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.