Strings Have Spin

If a string source is used to replace the conventional point-like source of gravitation in spacetime with torsion, then intrinsic spin arises naturally as an attribute of the string. This spin stems from the structure of the string, and not from internal motions.     

A family of strings with spin

Using an equivalence theorem, we discuss some stationary interiors for a string with spin density in a space with torsion. We show that there is a family of solutions characterized by the spin divergences and compare the solutions to string solutions in general relativistic spacetimes.     

Semiclassical backreaction around a nearly spinning cosmic string

This Letter investigates semiclassical backreaction of a conformally coupled massless scalar field on the geometrical background of a nearly spinning cosmic string — the spin density is smaller than, but arbitrarily close to, the dislocation parameter. As the spin density approaches the dislocation parameter, it is shown that an ergoregion spreads indefinitely around the cosmic string, boosting along the string axis the once static observers. Considering that the geometrical background contains closed timelike curves when the spin density exceeds the dislocation parameter, it is argued that the appearance of the ergoregion may be part of a chronology protection mechanism that takes place in related non-stationary geometries.     

How to lasso a plane gravitational wave

Beginning with the stress-energy tensor of an elastic string this paper derives a relativistic string and its form in a parallel transported Fermi frame including its reduction to a Cosserat string in the Newtonian limit. In a Fermi frame gravitational curvature is seen to induce three dominant relative acceleration terms dependent on: position, velocity and position, strain and position, respectively. An example of a string arranged in an axially flowing ring (a lasso) is shown to have a set of natural frequencies that can be parametrically excited by a monochromatic plane gravitational wave. The lasso also exhibits, in common with spinning particles, oscillations about geodesic motion in proportion to spin magnitude and wave amplitude when the spin axis lies in the gravitational wave front.     

Theta functions,modular invariance,and strings

We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.     

Spin chains and classical strings in two parameters q-deformed AdS3 × S3

In this paper, we study the spin chain and string excitation in the two-parameters q-deformed AdS₃ × S³ proposed by Hoare [6]. We obtain the deformed spin chain model at the fast spin limit for choices of deformed parameters. General ansatz for giant magnons are studied in great detail and complicated dispersion relation is treated perturbatively. We also study several types of hanging string solutions and their charges and spins are analyzed numerically. At last, we explore its pp-wave limit and find its solution only depends on the difference of deformed parameters.     

Entropy-vanishing transition and glassy dynamics in frustrated spins

In an effort to understand the glass transition, the dynamics of a nonrandomly frustrated spin model has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The slow dynamics can be associated with the presence of extended stringlike structures which demarcate regions of fast spin flips. An entropy-vanishing transition, with the string density as the order parameter, is related to the observed glass transition in the spin model.     

String order in half-integer-spin antiferromagnetic Heisenberg chains

We derive the extended string order parameter O(S) for antiferromagnetic Heisenberg chains with half-integer spin S in the valence-bond-solid picture. We obtain the analytic power-law scaling of O(S) versus the chain length L and show that O(S) scales at an extremely slow pace that decreases rapidly with growing spin magnitude. Furthermore, accurate numerical calculations show that the power-law scaling sets in only when L exceeds a characteristic length scale l(S) which increases very fast with growing S. Consequently, a pseudo-long-range string order exists in half-integer-spin Heisenberg chains. The implications of this result and its relationship to other topological features such as the end-chain states are discussed.     

Slow evolution of nearly-degenerate extremal surfaces

It was conjectured recently that the string worldsheet theory for the fast moving string in AdS times a sphere becomes effectively first order in the time derivative and describes the continuous limit of an integrable spin chain. In this paper we will try to make this statement more precise. We interpret the first order theory as describing the long term evolution of the tensionless string perturbed by a small tension. The long term evolution is a Hamiltonian flow on the moduli space of periodic trajectories. It should correspond to the renormgroup flow on the field theory side.     

D-branes from classical macroscopic strings

This paper is a sequel to the series of papers dedicated to model independent analysis of brane-like extended objects in curved backgrounds. In particular, we study cylindrical membranes wrapped around the extra compact dimension of a (D + 1)-dimensional Riemann–Cartan spacetime. The world-sheet equations are obtained from the universally valid conservation equations of the membrane stress–energy and spin tensors. In the limit of small extra dimension, the dimensionally reduced theory is obtained. The narrow membrane becomes an effective string characterized not only by tension and spin, but also by electric and dilaton charges. The boundary of such an effective string has been shown to live in less spacetime dimensions than its interior. Precisely, the string endpoints are trapped by the surfaces orthogonal to the gradient of the effective dilaton field. The string dynamics has been shown to follow from an action functional subject to the Dirichlet boundary conditions. This way, we have succeeded in obtaining a macroscopic D-brane analogue.     

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.     

Maxwell Equations in the Spinning Cosmic String Spacetimes

Maxwell equations are explicitly written in spin weighted form by using NP formalism in general flat spacetimes. Corresponding Maxwell equations are obtained in spinning and straight cosmic string backgrounds.     

Little heterotic strings

We discuss toroidal orbifolds of the E ₈×E ₈ heterotic string, in which the free-fermionic Higgs–matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider models in which some choices of the orbifold result in the projection of the graviton. In the models that we consider the projection also results in flipping the spin–statistics assignments in the massive string spectrum, whereas the massless spectrum retains the conventional spin–statistics assignments. We argue that the partition functions are mathematically consistent for one- and multi-loop amplitudes, owning to the existence of supersymmetry in the spectrum. A duality between different models at non-zero temperature is briefly discussed.     

Berry’s phase for a spin 1/2 particle in the presence of topological defects

The relativistic quantum dynamics of a spinorial quantum particle in the presence of a chiral conical background is investigated. We study the gravitational Berry geometric quantum phase acquired by a spin 1/2 particle in the chiral cosmic string spacetime. We obtain the result that this phase depends on the global features of this spacetime. We also consider the case that a string possesses an internal magnetic flux and obtain the geometric quantum phase in this case. The spacetime of multiple chiral cosmic strings is considered and the relativistic Berry quantum phase is also obtained.     

基于张量网络算法的自旋梯子系统的弦序参量的研究

通过基于矩阵乘积态(MPS)的强关联电子量子自旋梯子格点系统的张量网络(TN)算法,摸索研究自旋梯子量子多体系统的弦序参量,探测系统的量子相变点,刻画系统的量子临界现象,获取系统的量子相图,这为我们提供了一个研究自旋梯子系统的量子多体物理性质强有力的工具和方法:在不知道系统是否缺乏Landau对称性破缺序或者系统是否存在相关的拓扑弦序的情况下,可以先得到系统的基态波函数,如果基态缺乏Landau对称性破缺序,或可以通过其它方式找出系统存在若干非局域的弦序参量,来完整地描述一些拓扑量子相变点,获得系统的量子相图,从而丰富和发展了传统的Landau对称性破缺的相变理论.     

Convergence of Migdal-Kadanoff iterations: A simple and general proof

A short proof is presented showing convergence of Migdal-Kadanoff iterations for a large class of functions on compact connected Lie groups. From our estimate of the rate of convergence, we deduce lower bounds for string tension and mass gap in hierarchical four-dimensional lattice gauge and twodimensional spin models.     

Analytic relations between localizable entanglement and string correlations in spin systems

We study the relation between the recently defined localizable entanglement and generalized correlations in quantum spin systems. Differently from the current belief, the localizable entanglement is always given by the average of a generalized string. Using symmetry arguments we show that in most spin-1/2 and spin-1 systems the localizable entanglement reduces to the spin-spin or string correlations, respectively. We prove that a general class of spin-1 systems, which includes the Heisenberg model, can be used as a perfect quantum channel. These conclusions are obtained in analytic form and confirm some results found previously on numerical grounds.     

A spinning string

The Einstein-Cartan field equations are solved for a string source with spin-polarisation along the axis of symmetry. The interior solution is matched to an exterior vacuum space-time using Arkuszewski-Kopczyski-Ponomariev junction conditions. The exterior solution is a four dimensional extension of the space-time outside a spinning point particle in three dimensional Einstein theory. It reduces to the geometry outside a conventional straight cosmic string in the case of vanishing spin.