Relativistic String Research Articles

Thermal excitation spectrum from entanglement in an expanding quantum string

A surprising result in e+e− collisions is that the particle spectra from the string formed between the expanding quark–antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time τ, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature Tτ=ħ/(2πkBτ), even in the absence of any scatterings.

Second quantization of a covariant relativistic spacetime string in Steuckelberg–Horwitz–Piron theory

A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg [Helv. Phys. Acta 14, 588 (1941)], and further developed by Horwitz and Piron [Helv. Phys. Acta 46, 316 (1973)], and discussed at length in the book of Horwitz [Relativistic Quantum Mechanics, Springer (2015)]. We describe the space-time string using the solutions of relativistic harmonic oscillator [J. Math. Phys. 30, 66 (1989)]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.

Boundary operators in effective string theory

Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are relevant for the controlled study of open relativistic strings with freely moving endpoints. Relativistic open strings are thought to encode the dynamics of confined quark-antiquark pairs in gauge theories in the planar approximation. Neumann boundary operators can be organized by their behavior under scaling of the target space coordinates Xμ, and the set of allowed X-scaling exponents is bounded above by +1/2 and unbounded below. Negative contributions to X-scalings come from powers of a single invariant, or “dressing” operator, which is bilinear in the embedding coordinates. In particular, we show that all Neumann boundary operators are dressed by quarter-integer powers of this invariant, and we demonstrate how this rule arises from various ways of regulating the short-distance singularities of the effective theory.

Extended Galilean symmetries of non-relativistic strings

We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.

Dynamics of Carroll strings

We construct the canonical action of a Carroll string doing the Carroll limit of a canonical relativistic string. We also study the Killing symmetries of the Carroll string, which close under an infinite dimensional algebra. The tensionless limit and the Carroll $p$-brane action are also discussed.

Global existence of smooth solutions to relativistic string equations in Schwarzschild space-time for small initial data

This paper is concerned with the motion of relativistic strings in Schwarzschild space-time. In a general framework, we first analyze the basic equations for the motion of a [Formula: see text]-dimensional extended object in a general enveloping space-time [Formula: see text], which is a given Lorentzian manifold, and then we investigate some important properties enjoyed by the equations for the motion of relativistic strings in Schwarzschild space-time. In particular, the equations are shown to form a totally linearly degenerate system of first-order hyperbolic equations in [Formula: see text] dimensions. Based on this observation and under suitable assumptions, we are able to prove the global existence of smooth solutions to the Cauchy problem for the equations of motion of relativistic strings (in Schwarzschild space-time) with sufficiently small arc length.

Towards a theory of the QCD string

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to $Q=\sqrt{7\over 16\pi}\approx 0.37$. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in $SU(3)$ and $SU(5)$ gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to $Q_L\approx0.38\pm0.04$.

Matrix Mechanics of the Relativistic Point Particle and String in Clifford Space

We resolve the space-time canonical variables of the relativistic point particle into inner products of Weyl spinors with components in a Clifford algebra and find that these spinors themselves form a canonical system with generalized Poisson brackets. For N particles, the inner products of their Clifford coordinates and momenta form two NxN Hermitian matrices X and P which transform under a U(N) symmetry in the generating algebra. This is used as a starting point for defining matrix mechanics for a point particle in Clifford space. Next we consider the string. The Lorentz metric induces a metric and a scalar on the world sheet which we represent by a Jackiw-Teitelboim term in the action. The string is described by a polymomenta canonical system and we find the wave solutions to the classical equations of motion for a flat world sheet. Finally, we show that the SL(2.C) charge and space-time momentum of the quantized string satisfy the Poincare algebra.

Bose-Einstein condensate strings

We consider the possible existence of gravitationally bound general relativistic strings consisting of Bose-Einstein condensate (BEC) matter which is described, in the Newtonian limit, by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. In the Madelung representation of the wave function, the quantum dynamics of the condensate can be formulated in terms of the classical continuity equation and the hydrodynamic Euler equations. In the case of a condensate with quartic nonlinearity, the condensates can be described as a gas with two pressure terms, the interaction pressure, which is proportional to the square of the matter density, and the quantum pressure, which is without any classical analogue, though, when the number of particles in the system is high enough, the latter may be neglected. Assuming cylindrical symmetry, we analyze the physical properties of the BEC strings in both the interaction pressure and quantum pressure dominated limits, by numerically integrating the gravitational field equations. In this way we obtain a large class of stable stringlike astrophysical objects, whose basic parameters (mass density and radius) depend sensitively on the mass and scattering length of the condensate particle, as well as on the quantum pressure of the Bose-Einstein gas.

Improving cosmic string network simulations

In real-time lattice simulations of cosmic strings in the Abelian Higgs model, the broken translational invariance introduces lattice artifacts; relativistic strings therefore decelerate and radiate. We introduce two different methods to construct a moving string on the lattice, and study in detail the lattice effects on moving strings. We find that there are two types of lattice artifact: there is an effective maximum speed with which a moving string can be placed on the lattice, and a moving string also slows down, with the deceleration approximately proportional to the exponential of the velocity. To mitigate this, we introduce and study an improved discretization, based on the tree-level L\uscher-Weisz action, which is found to reduce the deceleration by an order of magnitude, and to increase the string speed limit by an amount equivalent to halving the lattice spacing. The improved algorithm is expected to be very useful for 3D simulations of cosmic strings in the early Universe, where one wishes to simulate as large a volume as possible.

Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings: Finite volume size effects

We study Kelvin modes and translational zero modes excited along a quantized vortex and relativistic global string in superfluids and a relativistic field theory, respectively, by constructing the low-energy effective theory of these modes. We find that they become exact gapless Nambu-Goldstone modes only in a system with infinite volume limit. On the other hand, in a system with the finite volume, we find an imaginary massive gap causing the tachyonic instability above some critical wavelength in the relativistic theory. We also find in the non-relativistic theory that Kelvin modes with wavelengths longer than some critical value propagate in the direction opposite to those with shorter length, contrary to conventional understanding. The number of Nambu-Goldstone modes also saturate the equality of the Nielsen-Chadha inequality for both relativistic and non-relativistic theories.

Motion of Relativistic Strings on the Equatorial Plane in the Schwarzschild Space-Time

In this paper, we investigate the basic equations of the motion for relativistic strings on the equatorial plane in the Schwarzschild space-time, discuss smooth solutions of the motion equations for closed strings, and obtain some interesting physical results.

Effective string theory revisited

We revisit the effective field theory of long relativistic strings such as confining flux tubes in QCD. We derive the Polchinski-Strominger interaction by a calculation in static gauge. This interaction implies that a non-critical string which initially oscillates in one direction gets excited in orthogonal directions as well. In static gauge no additional term in the effective action is needed to obtain this effect. It results from a one-loop calculation using the Nambu-Goto action. Non-linearly realized Lorentz symmetry is manifest at all stages in dimensional regularization. We also explain that independent of the number of dimensions non-covariant counterterms have to be added to the action in the commonly used zeta-function regularization.

Ratio of decay widths ofX(3872)toψ′γandJ/ψγas a test of theX(3872)dynamical structure

Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the coupled-channel approach, where the $c\bar c$ states are described by relativistic string Hamiltonian, while for the decay channels $DD^*$ a string breaking mechanism is used. Within this method a sharp peak and correct mass shift of the $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was already obtained for a prescribed channel coupling to the $DD^*$ decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction $c_1=0.153 (\theta=8.8^\circ$), which increases the transition rate $\Gamma(X(3872)\rightarrow J/\psi\gamma)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow \psi^{\prime}\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi \gamma)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state.

Lorentzian varifolds and applications to relativistic strings

We develop a suitable generalization of Almgren's theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in lorentzian minimal surfaces, we introduce, within the varifold class, various notions of generalized minimal timelike submanifolds of arbitrary codimension in flat Minkowski spacetime, which are global in character and admit conserved quantities, such as relativistic energy and momentum. In particular, we show that stationary lorentzian 2-varifolds properly include the class of classical relativistic and subrelativistic strings. We also discuss several

Lorentz violation, two-time physics, and strings

The aim of this paper is to study the generalization of the relativistic particle recently proposed by Kostelecký. An alternative action for this system is presented, and it is shown that this action can be interpreted as a particle in curved space. Furthermore, the following results are established for the model: (i) there exists a limit where the system has more local symmetries than the usual relativistic particle; (ii) in this limit when Lorentz symmetry is restored, a direct relationship with the two-time physics is determined; (iii) if also Poincaré symmetry is recovered, the action of a relativistic bosonic string is obtained.

Radial Regge trajectories for higher ψ(nS) and ψ(nD) states

The masses of $\psi((n+1) {}^3S_1)$ and $\psi(n {}^3D_1)$ are calculated using the relativistic string Hamiltonian with "linear+gluon-exchange" potential. They occur in the range 4.5-5.8 GeV, in particular, $M(3D)=4.54$ GeV, $M(5S)=4.79$ GeV, $M(4D)=4.85$ GeV are calculated with accuracy $\sim 50$ MeV. Linear Regge trajectories: $M^2(nS)=M^2(\psi(4.42))+ 2.91$ GeV$^2 (n-4)$ $(n\geq 4) $ and $M^2(nD)=(4.54^2+ 2.88 (n-3))$ GeV$^2$ ($n\geq 3$) are obtained only for higher charmonium excitations. They have slopes two times larger than those of light mesons and give good description of calculated masses. These masses are compared with enhancements in some recent $e^+e^-$ experiments.

Holographic dual of collimated radiation

We propose a new and simple method of estimating the radiation due to an accelerated quark in a strongly coupled medium, within the framework of the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. In particular, we offer a heuristic explanation of the collimated nature of synchrotron radiation produced by a circling quark, which was recently studied by Athanasiou et al (2010 Phys. Rev. D 81 26001). The gravitational dual of such a quark is a coiling string in AdS, whose backreaction on the spacetime geometry remains tightly confined, as if ‘beamed’ towards the boundary. While this appears to contradict conventional expectations from the scale/radius duality, we resolve the issue by observing that the backreaction of a relativistic string is reproduced by a superposition of gravitational shock waves. We further demonstrate that this proposal allows us to reduce the problem of computing the boundary stress tensor to merely calculating geodesics in AdS, as opposed to solving linearized Einstein's equations.

T-duality for string in Hořava–Lifshitz gravity

We continue our study of the Lorentz breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz breaking string theories and show that they are the same as that of Buscher's T-duality for the relativistic strings.

The2−+assignment for theX(3872)

Very recently the BaBar collaboration has put forward a claim that the X(3872) is not a 1^++ resonance, as most of the phenomenological work on the subject was relying on, but rather a 2^-+ one. We examine the consequences of this quantum number assignment for the solution of the X(3872) puzzle. The molecular interpretation appears less likely, and the conventional charmonium interpretation should be reconsidered. There are several well-known difficulties with this interpretation, to which we add a new one: the production cross section at CDF is predicted to be much smaller than that observed. We also confirm, using a relativistic string model, the conclusion from potential models that the mass of the state is not consistent with expectations. In the tetraquark interpretation the 2^-+ assignment implies a rich spectrum of partner states, although the X(3872) may be among the few which are narrow enough to be observable.