Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

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.     

Gauge unification in type I/I′ models

We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gauge mediated supersymmetry breaking on the “visible” brane with a dangerously low scale of supersymmetry breaking. Evading these problems in low string scale models requires a departure from the MSSM structure, which would imply that the success of gauge unification in the MSSM is just an accident.     

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.     

电子小提琴与常规小提琴的无线载波传输演示

小提琴可分解成拉弦系统和共振箱系统．在拉弦系统中,弦的振动被变为电声信号,以电磁波的形式发射到空中．在共振箱系统中,由调频接收器接收信号,经电声转换后驱动共鸣箱发声．改装后的电子小提琴可用于物理实验演示教学及小提琴弦振动和共鸣箱的频谱分析．     

Superstrings in Curved Ramond-Ramond Backgrounds

We discuss the main issues related to understanding closed string spectrum in Ramond-Ramond backgrounds on the example of AdS₅ × S ⁵ and and its special limit – the maximally supersymmetric plane-wave background with constant null 5-form field strength. As we describe, in the latter case the spectrum can be found explicitly. We compare the plane-wave string spectrum with the expected form of the light-cone gauge spectrum of the AdS₅ × S ⁵ superstring and comment on the tensionless string limit.     

Fine structure of the string spectrum in <Emphasis Type="Italic">AdS</Emphasis><Subscript>5</Subscript> × <Emphasis Type="Italic">S</Emphasis><Superscript>5</Superscript>

The spectrum of an infinite spinning string in AdS ₅ does not precisely match the spectrum of dual gauge theory operators, interpolated to the strong coupling regime with the help of Bethe-ansatz equations. We show that the mismatch is due to interactions in the string σ-model which cannot be neglected even at asymptotically large’ t Hooft coupling.     

String deformations induced by retardation effects in mesons

The rotating-string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a method to estimate the retardation effects in this model, but the string was still kept straight. We now go a step further and show that this kind of retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.     

Exciting the GKP string at any coupling

We analyze the spectrum of excitations around the Gubser-Klebanov-Polyakov (GKP) rotating string in the long string limit and construct a parametric representation for their dispersion relations at any value of the string tension. On the gauge theory side of the AdS/CFT correspondence, i.e., in the planar N=4 super Yang-Mills theory, the problem is equivalent to finding the spectrum of scaling dimensions of large spin, single-trace operators. Their scaling dimensions are obtained from the analysis of the Beisert-Staudacher asymptotic Bethe ansatz equations, which are believed to solve the spectral problem of the planar gauge theory. We examine the resulting dispersion relations in various kinematical regimes, both at weak and strong coupling, and detail the matching with the Frolov-Tseytlin spectrum of transverse fluctuations of the long GKP string. At a more dynamical level, we identify the mechanism for the restoration of the SO(6) symmetry, initially broken by the choice of the Berenstein-Maldacena-Nastase vacuum in the Bethe ansatz solution to the mixing problem.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

Instability of string models of baryons: Character and manifestations

The character of the instability of a rotational state (rotation of the system at a constant speed) against small perturbations is studied in detail for the Y string model of the baryon. It is shown that the existing instability is due to the presence of repeated real-valued frequencies in the spectrum of small perturbations and that there are no complex-valued frequencies in this spectrum. This leads to a linear growth of small-perturbation amplitudes. A comparison of the Y configuration with the q-q-q linear string model of the baryon reveals a difference in the character of the instability of rotational states of these systems and in the manifestations of this instability. In particular, there are exponentially growing modes in the excitation spectrum of the linear model, which lead to an additional contribution to the baryon-state width.     

String creation and heterotic-type I′ duality

The BPS spectrum of type I′ string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I′, and it is demonstrated that the relevant states in type I′ preserve supersymmetry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the DOD8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I′, and on the predictions for the quantum mechanics of type I′ DO-branes.     

第六讲超弦理论与宇宙学的挑战

超弦理论从根本上改变了人们对时空的看法，时空在弦论中只是一种宏观体现．弦论中的非经典时空影响早期宇宙的发展，在一些观测宇宙学的实验中人们也许会发现弦论的效应，例如微波背景辐射的功率谱的反常．最近发现的暗能量也对弦论宇宙学提出了挑战．     

Spectrum generating algebra and no-ghost theorem for fermionic massive string

The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator.     

String-inspired model for orbital excitations of glueballs

The relativistic string-inspired model of glueballs which contain two valence gluons connected by a straight-line string, is constructed. The model spectrum which consists of five Regge trajectories is compared with the experimental data.     

Analysis of handling noises on wound strings

This study analyzes the handling noises that occur when a finger is slid along a wound string. The resulting noise has a harmonic structure due to the periodic texture of the wound string. The frequency of the harmonics and the root-mean-square amplitude of the noise were found to be linearly proportional to the sliding speed. In addition, the sliding excites the longitudinal modes of the string, thus resulting in a set of static harmonics in the noise spectrum. The sliding excites different longitudinal modes depending on the sliding location.     

The string of variable density: Further results

We analyze the problem of calculating the solutions and the spectrum of a string with arbitrary density and fixed ends. We build a perturbative scheme which uses a basis of WKB-type functions and obtain explicit expressions for the eigenvalues and eigenfunctions of the string. Using this approach we show that it is possible to derive the asymptotic (high energy) behavior of the string, obtaining explicit expressions for the first three coefficients (the first two can also be obtained with the WKB method). Finally, using an iterative approach we also obtain analytical expressions for the low energy behavior of the eigenvalues and eigenfunctions of a string with rapidly oscillating density, recovering (in a simpler way) results in the literature.     

String-inspired model for orbital excitations of glueballs

The relativistic string-inspired model of glueballs which contain two valence gluons connected by a straight-line string, is constructed. The model spectrum which consists of five Regge trajectories is compared with the experimental data.