Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.     

Moving Branes with Background Massless and Tachyon Fields in the Compact Spacetime

In this article, we shall obtain the boundary state associated with a moving Dp-brane in the presence of the Kalb–Ramond field B _μν , an internal U(1) gauge field A _α and a tachyon field, in the compact spacetime. According to this state, properties of the brane and a closed string, with mixed boundary conditions emitted from it, will be obtained. Using this boundary state, we calculate the interaction amplitude of two moving Dp ₁ and Dp ₂-branes with above background fields in a partially compact spacetime. They are parallel or perpendicular to each other. Properties of the interaction amplitude will be analyzed, and contribution of the massless states to the interaction will be extracted.     

Tachyon condensation and open string field theory

We perform canonical quantization of open string on a unstable D-brane in the background of tachyon condensation. Evaluating the Polyakov path-integral on a strip, we obtain a field theoretical propagator in the open string theory. As condensation occurs the string field theory is continuously deformed. At the infrared fixed point of condensation, the open string field on the unstable D-brane transmutes to that on the lower-dimensional D-brane with the correct D-brane tension.     

Resistance of a rotating-moving brane with background fields against collapse

Using the boundary state formalism we investigate the effect of tachyon condensation process on a rotating and moving Dp$p$-brane with various background fields in the bosonic string theory. The rotation and motion are inside the brane volume. We demonstrate that some specific rotations and/or motions can preserve the brane from instability and collapse.     

Noncommutative Dp-Brane in General Background Fields

We investigate the noncommutativity of open strings, attached to a Dp-brane, in the presence of the linear dilaton, tachyon, U(1) gauge field as well as constant antisymmetric B-field backgrounds. The Noncommutativity parameter, open string metric, and some special cases will be studied. The Mode-dependent noncommutativity, inspired by the tachyon field, will be discussed in detail.     

Tadpole resummations in string theory

While R–R tadpoles should be canceled for consistency, string models with broken supersymmetry generally have uncanceled NS–NS tadpoles. Their presence signals that the background does not solve the field equations, so that these models are in “wrong” vacua. In this Letter we investigate, with reference to some prototype examples, whether the true values of physical quantities can be recovered resumming the NS–NS tadpoles, hence by an approach that is related to the analysis based on String Field Theory by open–closed duality. We show that, indeed, the positive classical vacuum energy of a Dp-brane of the bosonic string is exactly canceled by the negative contribution arising from tree-level tadpole resummation, in complete agreement with Sen's conjecture on open-string tachyon condensation and with the consequent analysis based on String Field Theory. We also show that the vanishing classical vacuum energy of the SO(8192) unoriented bosonic open-string theory does not receive any tree-level corrections from the tadpole resummation. This result is consistent with the fact that this (unstable) configuration is free from tadpoles of massless closed-string modes, although there is a tadpole of the closed string tachyon. The application of this method to superstring models with broken supersymmetry is also discussed.     

Semiclassical bosonic <Emphasis Type="Italic">D</Emphasis>-brane boundary states in curved spacetime

In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g _AB and the constant antisymmetric Kalb-Ramond field b _AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.     

Anisotropic evolution of a D-brane

The evolution of a probe D-brane in the p-brane background is considered. The anisotropic evolution of the world-volume of the D-brane with a given topology of a world-volume in the form of a direct product of a n-dimensional flat space and (3 − n)-dimensional sphere is formulated. In this case the anisotropy is described with the aid of two parameters (Hubble parameters) The special case of this evolution, namely the isotropic evolution corresponds to equality of these two parameters. In the latter case the masses and charges of the background p-branes are obtained.     

Nonassociative Star Product Deformations for D-Brane World-Volumes in Curved Backgrounds

We investigate the deformation of D-brane world-volumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain the world-volume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture that unfolds is the following: when the gauge invariant combination ω=B+F is constant one obtains the standard Moyal deformation of the brane world-volume. Similarly, when dω= 0 one obtains the noncommutative Kontsevich deformation, physically corresponding to a curved brane in a flat background. When the background is curved, H=dω≠ 0, we find that the relevant algebraic structure is still based on the Kontsevich expansion, which now defines a nonassociative star product with an A _∞ homotopy associative algebraic structure. We then recover, within this formalism, some known results of Matrix theory in curved backgrounds. In particular, we show how the effective action obtained in this framework describes, as expected, the dielectric effect of D-branes. The polarized branes are interpreted as a soliton, associated to the condensation of the brane gauge field. Received: 22 March 2001 / Accepted: 13 July 2001     

Dirac quantization of open p-brane

We give the scheme of Dirac quantization of open p-brane in the D-brane background. Treating the mixed boundary conditions as primary constraints, we get a set of secondary constraints, then the constraints conditions are shown to be equivalent to orbifold conditions imposed on normal p-brane modes.     

De Haas-van Alphen effect in unconventional superconductors

A theory of the de Haas-van Alphen effect in type-II p-wave and D-wave superconductors (the latter corresponds to the B _1g one-dimensional representation of group D _4h ) has been developed. Solutions for the order parameter and density of quasiparticle states near the upper critical field have been calculated. If the curve enclosing the extremal cross section of the Fermi surface in the plane perpendicular to the external magnetic field coincides with the line of nodes of the superconducting order parameter, the effect of the transition to the superconducting state on the amplitude of magnetization oscillations is negligible. If the line of nodes is oriented differently with respect to the applied magnetic field, the de Haas-van Alphen oscillations are suppressed in a manner qualitatively similar to the case of conventional superconductors. Zh. éksp. Teor. Fiz. 113, 2174–2192 (June 1998)     

Laser cooling of a single Ca+ ion: Observation of quantum jumps

This paper describes trapping and laser cooling of a Ca⁺ ion in an rf quadrupole ion trap. A single Ca⁺ ion is laser cooled to below 130 mK and quantum jumps are observed by exciting the ion into the metastable D _5/2 state via the P _3/2 state. The lifetime of the metastable D _5/2 state is estimated from the distribution of the dark periods of the quantum-jump signal. Collision-induced jumps between the metastable D _3/2 state and the D _5/2 state in a background gas are also directly observed.     

Symplectic quantization of open strings in constant background <Emphasis Type="Italic">B</Emphasis>-field

The symplectic quantization (Faddeev-Jackiw) method is reviewed briefly, and then it is applied to the open strings in the D-brane background with a non-vanishing constant B-field. We shall work in the discrete version, and the reduced phase space is obtained directly by solving the mixed boundary conditions. The non-commutativity of coordinates along the D-brane is reproduced. Some ambiguities in the previous papers could be avoided by this method. Received: 3 April 2003, Revised: 18 April 2003, Published online: 18 June 2003     

Spacelike brane actions

We derive effective actions for "spacelike branes" (S-branes) and find a solution describing the formation of fundamental strings in the rolling tachyon background. The S-brane action is a Dirac-Born-Infeld action for Euclidean world volumes defined in the context of time-dependent tachyon condensation of non-BPS (Bogomol'nyi-Prasad-Sommerfield) branes. It includes gauge fields and, in particular, a scalar field associated with translation along the time direction. We show that the BIon spike solutions constructed in this system correspond to the production of a confined electric flux tube (a fundamental string) at late time of the rolling tachyon.     

Quantum Symmetries and Exceptional Collections

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the \mathbb Z₅{{\mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.     

AdS braneworld with backreaction

We review the tachyon model derived from the dynamics of a 3-brane moving in the AdS₅ bulk. The bulk geometry is based on the Randall-Sundrum II model extended to include the radion. The effective tachyon Lagrangian is modified due to the back-reaction of the brane on the bulk geometry.     

A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = C _γ ρ ^γ for γ > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied.     

Tachyons, Lamb shifts and superluminal chaos

An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 keV/c² and estimate the tachyonic coupling strength to subluminal matter. The impact of the tachyon field on ground state hyperfine transitions in hydrogen and muonium is investigated. Bounds on atomic transition rates effected by tachyon radiation as well as estimates on the spectral energy density of a possible cosmic tachyon background radiation are derived. Received 13 August 1999 and Received in final form 7 February 2000     

The effective use of precision electroweak measurements

Bound state population dynamics in a diatom modelled by an appropriate Morse oscillator with a time-dependent well-depth is investigated perturbatively both in the absence and presence of high intensity radiation. For sinusoidally oscillating well-depth, the population of themth bound vibrational level,P _mm(t), is predicted to be a parabolic function of the amplitude of the oscillation of the well-depth (ΔD ₀) at a fixed laser intensity. For a fixed value of ΔD ₀,P _mm(t) is also predicted to be quadratic function of the field intensity (ɛ ₀). Accurate numerical calculations using a time-dependent Fourier grid Hamiltonian (TDFGH) method proposed earlier corroborate the predictions of perturbation theory. As to the dissociation dynamics, the numerical results indicate that the intensity threshold is slightly lowered if the well-depth oscillates. Possibility of the existence of pulse-shape effect on the dissociation dynamics has also been investigated.     

Tachyon bound state in Yang-Mills theory and instability of the vacuum

Existence of the tachyon bound state in a Yang-Mills system is discussed using the ladder approximation for the BS equation. Due to the attractive force between two massless gauge fields in the group singlet channel a tachyon pole is formed for whatever small coupling constant. The normal vacuum is expected to be unstable with respect to the condensation of this tachyon field.