Non-archimedean strings

A full set of factorized, dual, crossing-symmetric tree-level N-point amplitudes is constructed for non-archimedean closed strings. Momentum components and space-time coordinates are still valued in the field of real numbers, quantum amplitudes in that of complex numbers. It is the world-sheet parameters, which one integrates over, that become p-adic. For the closed string the parameters are valued in quadratic extensions of the fields Q_p of p-adic numbers (p = prime).     

Tachyon dynamics in string theory

We summarize the recent developments in the study of time dependent solutions describing the rolling of a tachyon on a non-BPS D-brane system.     

Non-archimedean strings and Bruhat-Tits trees

It is shown that the Bruhat-Tits tree for thep-adic linear groupGL(2) is a natural non-archimedean analog of the open string world sheet. The boundary of the tree can be identified with the field ofp-adic numbers. We construct a lattice quantum field theory on the Bruhat-Tits tree with a simple local lagrangian and show that it leads to the Freund-Olson amplitudes for emission processes of the particle states from the boundary.     

Classical string dynamics with non-trivial topology

The possibility of branching processes for classical strings is investigated on the basis of the Nambu-Goto action. We parametrize the world sheet by a Riemann surface M and introduce a degenerate, semi-Riemannian metric η on M. Well-known results about the conformal group Diff(S¹) × Diff(S¹) are generalized to the case of (M, η). We provide an infinite dimensional Hamiltonian setting for branching processes of strings. Finally, the classical background for the theory of quantum strings as developed by Krichever and Novikov is discussed within this classical framework.     

Classical geometry of bosonic string dynamics

We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase-space approach to classical field theory put forward by Kijowski, Tulczyjew, and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e., isometries of the underlying spacetime. Thus, the symmetries of relativistic mechanics coming from Killing tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space.     

Holography and string dynamics in time-dependent backgrounds

We study the dynamics of D-branes in a smooth time-dependent background. The theory on the branes is a time-dependent noncommutative field theory. We find the metric and fluxes that determine the dual holographic closed string theory. This provides a concrete example of holography in a cosmological setting.     

The dynamics of a twistable relativistic string

Following a suggestion of Kraemmer and Nielsen the possibility that the dual fermion model may be obtained by quantising a classical theory of a twistable string is discussed. Quantisation conditions are obtained which, for one value of a dimensionless constant ?/β, are represented by this dual model, but in consequence the classical limit cannot be taken without departing from the model. The appropriate representation of the algebra of Virasoro gauge conditions is obtained but the additional fermion gauge conditions would seem to be a quantum phenomenon in this picture.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

Long string dynamics in pure gravity on AdS3

Journal of Experimental and Theoretical Physics - We study the classical dynamics of a completion of pure AdS3 gravity, whose only degrees of freedom are boundary gravitons and long strings. We...     

Classical dynamics of the rigid string from the Willmore functional

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into a space of constant curvature. It is shown that the rigid string in flat space-time is described by the Euler-Lagrange equation for the Willmore functional in a space-time of constant curvature K = −γ/(2α), where γ and α are constants in front of the Nambu-Goto term and the curvature term in the rigid string action, respectively. For simplicity the Euclidean version of the rigid string in three-dimensional space-time is considered. The Willmore functional (the action for the “Willmore string”) is obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for the rigid string. Such a “reduction” of the rigid string model would be useful, for example, by applying some results about the Nambu-Goto string dynamics in the de Sitter universe to the rigid string model in the Minkowski space-time. It also allows us to use numerous mathematical results about Willmore surfaces in the context of the physical problem.     

Quantum dynamics of a massless relativistic string (II)

The massless relativistic free string is studied in the gauge x₀ = τ. It is found that the classical solutions include transverse and longitudinal vibrations. The problem is treated both in the Lagrangian and Hamiltonian formalism. Different ways of quantizing the system are investigated. The path integral quantization leads to a Poincaré invariant quantum theory in any number of dimensions.     

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparameterization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are derived. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.     

Instability of the Y string baryon model within classical dynamics

For the three-string baryon model (Y configuration), the known exact solution to the classical equations of motion that describes the rotational motion of the system at a constant speed is investigated for stability. In the spectrum of small perturbations of this solution, modes growing exponentially with time are found, whereby the instability of rotational motion is proven for the Y configuration. This result is confirmed within an alternative approach that makes it possible to determine the classical motion of the system from a specific initial position and initial velocities of string points. A comparison of the Y configuration with the model of a relativistic string with massive ends, in which case rotational motion is stable in the linear approximation, aids in revealing the most adequate string model from the point of view of describing baryon excitations on Regge trajectories.     

Comment on the proper QCD string dynamics in a heavy-light system

The string correction to the interquark interaction at large distances is derived using the field theory approach to a heavy-light quark-antiquark system in the modified Fock-Schwinger gauge.     

Delay-induced dynamics of an axially moving string with direct time-delayed velocity feedback

The local dynamics of an axially moving string under aerodynamic forces is investigated with a time-delayed velocity feedback controller. The retarded differential difference governing equation is obtained in modal coordinates of a two-degree-of-freedom system through Galerkin’s discretization procedure. The stability of trivial equilibrium is examined with the change of counting multiplicity of eigenvalue with positive real part. The Hopf bifurcation curves are determined in the controlling parameter spaces. With the aid of the center manifold reduction, a functional analysis is carried out to reduce the modal equation to a single ordinary differential equation of one complex variable on the center manifold. The approximate analytical solutions in the vicinity of Hopf bifurcations are derived in the case of primary resonance. The curves of excitation-response and frequency-response curves are shown with the effect of time delay. The stability analysis for steady-state periodic solutions of the reduced system indicates the onset of local control parameter for vibration control and response suppression. Moreover, the Poincaré-Bendixson theorem and energy considerations are used to investigate the existences and characteristics of quasi-periodic solutions when stability of the periodic solution is lost. Numerical results demonstrate the validity of the analytical prediction. Two different kinds of quasi-periodic solutions are found.