Circular String Research Articles

Twistorial analyticity and three stringy systems of the Kerr spinning particle

The Kerr spinning particle has a remarkable analytical twistorial structure. Analyzing electromagnetic excitations of the Kerr circular string which are aligned to this structure, we obtain a simple stringy skeleton of the spinning particle which is formed by a topological coupling of the Kerr circular singular string and by an axial singular stringy system. We show that the chiral traveling waves, related to an orientifold world-sheet of the axial stringy system, are described by the massive Dirac equation, so we argue that the axial string may play the part of a stringy carrier of wave function and play also a dominant role in the scattering processes. A key role of the third, {\it complex} Kerr string is discussed. We conjecture that it may be one more alternative to the Witten twistor string, and a relation to the spinor helicity formalism is also discussed.

Tube of (circle F, D0, D2) bound state in Melvin background

By using the Born–Infeld action we show that the m circular fundamental strings, n D2-branes and k D0-branes could become a tubular bound state which is prevented from collapsing by the magnetic force in the Melvin background. However, if the ratio m/n is larger then a critical value the tube will become unstable and collapse to zero radius. We make analyses to find the critical value and tube radius therein. The tube configurations we found are different from the well-known tubular bound states of straight fundamental strings, D0- and D2-branes, which are supported by the angular momentum.

Semiclassical spinning strings and confining gauge theories

We study multi-charged rotating string states on type IIB regular backgrounds dual to confining SU( N) gauge theories with (softly broken) N=1 supersymmetry, in the infra red regime. After exhibiting the classical energy/charge relations for the folded and circular two-charge strings, we compute in the latter case the one loop sigma-model quantum correction. The classical relation has an expansion in positive powers of the analogous of the BMN effective coupling, while the quantum corrections are non-perturbative in nature and are not subleading in the limit of infinite charge. We comment about the dual field theory multi-charged hadrons and the implications of our computation for the AdS/ N=4 duality.

Generalized pulsating strings

In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius integrable system and the corrections to the energy. To do that we use the approach developed by Minahan in hep-th/0209047 and find that the corrections are quite different from those obtained in that paper and hep-th/0310188. We conclude with comments on our solutions and obtained corrections to the energy, expanded to the leading order in lambda.

The SU(3) spin chain sigma model and string theory

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N=4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular strings with angular momenta along three orthogonal directions of the five-sphere is reproduced as a particular case from the spin chain sigma model.

Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings

We present new self-gravitating solutions in five dimensions that describe circular strings, i.e., rings, electrically coupled to a two-form potential (as e.g., fundamental strings do), or to a dual magnetic one-form. The rings are prevented from collapsing by rotation, and they create a field analogous to a dipole, with no net charge measured at infinity. They can have a regular horizon, and we show that this implies the existence of an infinite number of black rings, labeled by a continuous parameter, with the same mass and angular momentum as neutral black rings and black holes. We also discuss the solution for a rotating loop of fundamental string. We show how more general rings arise from intersections of branes with a regular horizon (even at extremality), closely related to the configurations that yield the four-dimensional black hole with four charges. We reproduce the Bekenstein-Hawking entropy of a large extremal ring through a microscopic calculation. Finally, we discuss some qualitative ideas for a microscopic understanding of neutral and dipole black rings.

Three-spin strings on AdS5×S5 from [formula omitted] SYM

Using the integrable spin chain picture we study the one-loop anomalous dimension of certain single trace scalar operators of N=4 SYM expected to correspond to semi-classical string states on AdS5×S5 with three large angular momenta (J1,J2,J3) on S5. In particular, we investigate the analyticity structure encoded in the Bethe equations for various distributions of Bethe roots. In a certain region of the parameter space our operators reduce to the gauge theory duals of the folded string with two large angular momenta and in another region to the duals of the circular string with angular momentum assignment (J,J′,J′), J>J′. In between we locate a critical line. We propose that the operators above the critical line are the gauge theory duals of the circular elliptic string with three different spins and support this by a perturbative calculation.

Counting Strings with Given Elementary Symmetric Function Evaluations II: Circular Strings

Let $\alpha$ be a string over an alphabet that is a finite ring, $R$. The $k$th elementary symmetric function evaluated at $\alpha$ is denoted $T_k(\alpha)$. In a companion paper we studied the properties of $\mathbf{S}_R(n;\tau_1,\tau_2,\ldots,\tau_k)$, the set of length $n$ strings for which $T_i(\alpha) = \tau_i$. Here we consider the set, $\mathbf{L}_R(n;\tau_1,\tau_2,\ldots,\tau_k)$, of equivalence classes under rotation of aperiodic strings in $\mathbf{S}_R(n;\tau_1,\tau_2,\ldots,\tau_k)$, sometimes called Lyndon words. General formulae are established and then refined for the cases where $R$ is the ring of integers $\Z{q}$ or the finite field $\F{q}$.

Yang-Mills duals for semiclassical strings onAdS5×S5

We consider a semiclassical multiwrapped circular string pulsating on S_5, whose center of mass has angular momentum J on an S_3 subspace. Using the AdS/CFT correspondence we argue that the one-loop anomalous dimension of the dual operator is a simple rational function of J/L, where J is the R-charge and L is the bare dimension of the operator. We then reproduce this result directly from a super Yang-Mills computation, where we make use of the integrability of the one-loop system to set up an integral equation that we solve. We then verify the results of Frolov and Tseytlin for circular rotating strings with R-charge assignment (J',J',J). In this case we solve for an integral equation found in the O(-1) matrix model when J'< J and the O(+1) matrix model if J'> J. The latter region starts at J'=L/2 and continues down, but an apparent critical point is reached at J'=4J. We argue that the critical point is just an artifact of the Bethe ansatz and that the conserved charges of the underlying integrable model are analytic for all J' and that the results from the O(-1) model continue onto the results of the O(+1) model.

Vorton existence and stability.

We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about vorton solutions and, in particular, their analytic stability with respect to a range of radial and nonradial perturbations. We then discuss numerical results of vorton simulations in a full 3D field theory, that is, Witten's original bosonic superconducting string model with a modified potential term. For specific parameter values, these simulations demonstrate the long-term stability of sufficiently large vorton solutions created with an elliptical initial ansatz.

Circular semiclassical string solutions on AdS5× S5

We discuss two semiclassical string solutions on AdS 5× S 5. In the first case, we consider a multiwrapped circular string pulsating in the radial direction of AdS 5, but fixed to a point on the S 5. We compute the energy of this motion as a function of a large quantum number n. We identify the string level with mn, where m is the number of string wrappings. Using the AdS/CFT correspondence, we argue that the bare dimension of the corresponding gauge invariant operator is 2 n and that its anomalous dimension scales as λ 1/4 mn , for large n. Next we consider a multiwrapped circular string pulsating on the S 5. We compute the energy of this motion as a function of a large quantum number, n where again the string level is given as mn. We find that the dimension of the corresponding operator is 2 n(1+ f( m 2 λ/(2 n) 2)), where f( x) is computible as a series about x=0 and where it is analytic. We also compare this result to the BMN result for large J operators.

Circular Semiclassical String solutions on Confining AdS/CFT Backgrounds

We study multiwrapped circular string pulsating in the radial direction of AdS black hole. We compute the energy of this string as a function of a large quantum number n. One then could associate it with energy and a quantum number of states in the dual finite temperature {\cal N}=4 SYM theory as well as three dimensional pure gauge theory. We observe that the n dependence of the energy has a universal form. We have also considered pulsating string in the background of the near-extremal D4-brane solution. Circular pulsating membrane in M-theory on AdS_7\times S^4 has also been studied.

Quantization of energy and writhe in self-repellingknots

Probably the most natural energy functional to be considered forknotted strings is that given by electrostatic repulsion. Inthe absence of counter-charges, a charged, knotted stringevolving along the energy gradient of electrostatic repulsionwould progressively tighten its knotted domain into a point on aperfectly circular string. However, in the presence of chargescreening self-repelling knotted strings can be stabilized.It is known that energy functionals in which repulsive forcesbetween repelling charges grow inversely proportionally to thethird or higher power of their relative distance stabilizeself-repelling knots. Especially interesting is the case of thethird power since the repulsive energy becomes scale invariantand does not change upon Möbius transformations(reflections in spheres) of knotted trajectories. We observehere that knots minimizing their repulsive Möbius energyshow quantization of the energy and writhe (measure ofchirality) within several tested families of knots.

Circular cosmic string loop in Brans-Dicke theory

The gravitational field of a stationary circular cosmic string loop, externally supported against collapse, is investigated in the context of Brans-Dicke theory in the weak field approximation of the field equations. The solution is quasi-conformally related to the corresponding solution in Einstein's General Relativity(GR) and goes over to the corresponding solution in GR when the Brans-Dicke parameter w becomes infinitely large.

Axion radiation from strings

This paper revisits the problem of the string decay contribution to the axion cosmological energy density. We show that this contribution is proportional to the average relative increase when axion strings decay of a certain quantity $N_{\rm ax}$ which we define. We carry out numerical simulations of the evolution and decay of circular and non-circular string loops, of bent strings with ends held fixed, and of vortex-antivortex pairs in two dimensions. In the case of string loops and of vortex-antivortex pairs, $N_{\rm ax}$ decreases by approximately 20%. In the case of bent strings, $N_{\rm ax}$ remains constant or increases slightly. Our results imply that the string decay contribution to the axion energy density is of the same order of magnitude as the well-understood contribution from vacuum realignment.

Quantum coherent string states inAdS3and theSL(2,R)Wess-Zumino-Witten-Novikov model

In this paper we make the connection between semiclassical string quantization and exact conformal field theory quantization of strings in 2+1 anti--de Sitter spacetime. More precisely, considering the Weiss-Zumino-Witten-Novikov model corresponding to $\mathrm{SL}(2,R)$ and its covering group, we construct quantum coherent string states, which generalize the ordinary coherent states of quantum mechanics, and show that in the classical limit they correspond to oscillating circular strings. After quantization, the spectrum is found to consist of two parts: A continuous spectrum of low mass states (partly tachyonic) satisfying the standard spin-level condition necessary for unitarity $|j|&lt;k/2,$ and a discrete spectrum of high mass states with asymptotic behavior ${m}^{2}{\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\propto}{N}^{2}$ $(N$ positive integer). The quantization condition for the high mass states arises from the condition of finite positive norm of the coherent string states, and the result agrees with our previous results obtained using semiclassical quantization. In the $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\infty}$ limit, all the usual properties of coherent or quasiclassical states are recovered. It should be stressed that we consider the circular strings only for simplicity and clarity, and that our construction can easily be used for other string configurations too. We also compare our results with those obtained in the recent paper by Maldacena and Ooguri, hep-th/0001053.

Splicing in abstract families of languages

We show that the iterated splicing operation determined by a regular H scheme (with some necessary restrictions) preserves membership in any full abstract family of languages. This involves translation of an H scheme into two alternative forms. The first form, which is closely related to the underlying biochemical operations, uses cutting and pasting rather than splicing. The second form uses matrices of languages, and in this formulation the splicing operation is translated into standard formal language operations (concatenation and quotient). Moreover, in the matrix formulation the splicing language itself may be expressed in terms of standard formal language operations, and this provides an algorithm for calculating the splicing language. As an application we use the cutting and pasting approach to extend the closure result to circular strings.

Chaotic scattering and capture of strings by a black hole

We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although it is a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition from order to chaos.

Self-gravitating cosmic rings

The classical Einstein-Maxwell field equations admit static horizonless wormhole solutions with only a circular cosmic string singularity. We show how to extend these static solutions to exact rotating asymptotically flat solutions. For a suitable range of parameter values, these solutions describe charged or neutral rotating closed cosmic strings, with a perimeter of the order of their Schwarzschild radius.

Quantum string dynamics in the conformal invariantSL(2,R)WZWN background: Anti–de Sitter space with torsion

We consider classical and quantum strings in the conformally invariant background corresponding to the $\mathrm{SL}(2,R)$ WZWN model. This background is locally anti--de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelizing. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both semi-classical and canonical string quantization, in order to see the effect of the conformal invariance of the background on the string mass spectrum. Both approaches yield that the high-mass states are governed by $m\ensuremath{\sim}\mathrm{HN}$ ($N\ensuremath{\in}{N}_{0},$ $N$ ``large''), where $m$ is the string mass and $H$ is the Hubble constant. It follows that the level spacing grows proportionally to ${N:d(m}^{2}{\ensuremath{\alpha}}^{\ensuremath{'}})/dN\ensuremath{\sim}N,$ while the string entropy goes like $S\ensuremath{\sim}\sqrt{m}.$ Moreover, it follows that there is no Hagedorn temperature, so that the partition function is well defined at any positive temperature. All results are compared with the analogue results in anti--de Sitter spacetime, which is a nonconformal invariant background. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conformal and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal backgrounds are identical. Interestingly enough, conformal invariance fixes the value of the spacetime curvature to be $\ensuremath{-}69/(26{\ensuremath{\alpha}}^{\ensuremath{'}}).$