Open String Ending Research Articles

Rotating Wilson loops and open strings in AdS3

The AdS/CFT correspondence relates super Yang–Mills on S3 to type IIB string theory on AdS5 × S5. In this context, a quark/anti-quark pair moving on an S1⊂S3 following prescribed trajectories is dual to an open string ending on the boundary of AdS3. In this paper we study the corresponding classical string solutions. The Pohlmeyer reduction reduces the equations of motion to a generalized sinh-Gordon equation. This equation includes, as particular cases, the Liouville equation as well as the sinh/cosh-Gordon equations. We study generic solutions of the Liouville equation and finite gap solutions of the sinh/cosh-Gordon ones. The latter ones are written in terms of Riemann theta functions. The corresponding string solutions are reconstructed giving new solutions and a broad understanding of open strings moving in AdS3. As a further example, the simple case of a rigidly rotating string is shown to exhibit these three behaviors depending on a simple relation between its angular velocity and the angular separation between its endpoints.

Closed string self-energy on the lightcone worldsheet lattice

We study the one loop correction to the closed bosonic string propagator, including the possible presence of D-branes, by discretizing the lightcone worldsheet on an $M\ifmmode\times\else\texttimes\fi{}N$ rectangular lattice, with $M\ensuremath{\propto}{P}^{+}$ and $N+1\ensuremath{\propto}i{x}^{+}$. The integrals over the moduli then become sums which we evaluate numerically. The main purpose of this study is to assess the reliability of the worldsheet lattice as a regulator of the divergences in string perturbation theory. There are two natural geometrical counterterms for the lightcone worldsheet, one proportional to the area of the worldsheet and the other proportional to the length of worldsheet boundaries, tracing the ends of open strings. We show that the divergences in the closed string self-energy can be cancelled by the area counterterm and a renormalization of the Regge slope parameter. The residual finite part is compatible with Lorentz invariance, provided a novel regularization, natural to the lightcone worldsheet lattice and described in this article, is employed.

OPEN STRING IN pp-WAVE BACKGROUND WITH B-FIELD

The open string ending on a flat D-brane in the pp-wave background with a constant B-field is exactly solvable but will be controlled by a more mass parameter. In this paper we mainly quantize this open string theory canonically by employing the Faddeev–Jackiw symplectic quantization procedure, and find that the phase space of the string coordinate and canonical momentum becomes fully noncummutative, consistent with the results obtained previously.

Zero modes for the boundary giant magnons

We study the fermion zero-mode dynamics for open strings ending on the giant graviton branes. For the open string ending on the Z=0 brane, the quantization of the fermion zero-modes of boundary giant magnons reproduces the 256 states of the boundary degrees with the precise realization of the SU(2|2)×SU(2|2) symmetry algebra. Also for the open string ending on the Y=0 brane, we reproduce the unique vacuum state from the fermion zero-modes.

Level-rank duality of untwisted and twisted D-branes of the [formula omitted] WZW model

We analyze the level-rank duality of untwisted and ε-twisted D-branes of the so ˆ ( N ) K WZW model. Untwisted D-branes of so ˆ ( N ) K are characterized by integrable tensor and spinor representations of so ˆ ( N ) K . Level-rank duality maps untwisted so ˆ ( N ) K D-branes corresponding to (equivalence classes of ) tensor representations onto those of so ˆ ( K ) N . The ε-twisted D-branes of so ˆ ( 2 n ) 2 k are characterized by (a subset of ) integrable tensor and spinor representations of so ˆ ( 2 n − 1 ) 2 k + 1 . Level-rank duality maps spinor ε-twisted so ˆ ( 2 n ) 2 k D-branes onto those of so ˆ ( 2 k ) 2 n . For both untwisted and ε-twisted D-branes, we prove that the spectrum of an open string ending on these D-branes is isomorphic to the spectrum of an open string ending on the level-rank-dual D-branes.

String and membrane condensation on three-dimensional lattices

In this paper, we investigate the general properties of latt ice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models which lead to Z2 gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first mode l contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open-strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a new type of topological order. PACS numbers: 11.15.-q,71.10.-w

Artificial light and quantum order in systems of screened dipoles

The origin of light is an unsolved mystery in nature. Recently, it was suggested that light may originate from a new kind of order, quantum order. To test this idea in experiments, we study systems of screened magnetic/electric dipoles in two-dimensional (2D) and 3D lattices. We show that our models contain an artificial light--a photonlike collective excitation. We discuss how to design realistic devices that realize our models. We show that the ``speed of light'' and the ``fine-structure constant'' of the artificial light can be tuned in our models. The properties of artificial atoms (bound states of pairs of artificial charges) are also discussed. The existence of artificial light (as well as artificial electron) in condensed-matter systems suggests that elementary particles, such as light and electron, may not be elementary. They may be collective excitations of quantum order in our vacuum. In our model, light is realized as a fluctuation of string-nets and charges as the ends of open strings (or nodes of string nets).

Noncommutative D-brane and open string in pp-wave background with B-field

The open string ending on a D-brane with a constant B-field in a pp-wave Ramond–Ramond background is exactly solvable. The theory is controlled by three dimensionful parameters: α′, the mass parameter (RR background times the lightcone momentum) and the B-field. We quantize the open string theory and determine the full noncommutative structure. In particular, we find a fully noncommutative phase space whose noncommutativity depends on all these parameters. The lightcone Hamiltonian is obtained, and as a consequence of the nontrivial commutation relations of the theory, new features of the spectrum are noted. Various scaling limits of the string results are considered. Physical implications are discussed.

The origin of noncommutativity?

Consistent boundary Poisson structures for open string theory coupled to background $B$-field are considered using the new approach proposed in hep-th/0111005. It is found that there are infinitely many consistent Poisson structures, each leads to a consistent canonical quantization of open string in the presence of background $B$-field. Consequently, whether the $D$-branes to which the open string end points are attached is noncommutative or not depends on the choice of a particular Poisson structure.

(1+p)-dimensional open D(p−2) brane theories

The dynamics of a Dp brane can be described either by an open string ending on this brane or by an open D(p - 2) brane ending on the same Dp brane. The ends of the open string couple to a Dp brane worldvolume gauge field while the boundary of the open D(p - 2) brane couples to a (p - 2)-form worldvolume potential whose field strength is Poincare dual to that of the gauge field on the Dp-brane worldvolume. With this in mind, we find that the Poincare dual of the fixed rank-2 magnetic field used in defining a (1 + p)-dimensional noncommutative Yang-Mills (NCYM) gives precisely a near-critical electric field for the open D(p - 2) brane. We therefore find (1 + p)-dimensional open D(p - 2) brane theories along the same line as for obtaining noncommutative open string theories (NCOS), OM theory and open Dp brane theories (ODp) from NS5 brane. Similarly, the Poincare dual of the near-critical electric field used in defining a (1 + p)-dimensional NCOS gives a fixed magnetic-like field. This field along with the same bulk field scalings defines a (1 + p)-dimensional noncommutative field theory. In the same spirit, we can have various (1 + 5)-dimensional noncommutative field theories resulting from the existence of ODp if the description of open D(4 - p) brane ending on the NS5 brane is insisted.

Noncommutative D-Brane in a Nonconstant NS-NSBField Background

We show that, when the field strength H of the NS-NS B field does not vanish, the coordinates x and momenta p of open string end points satisfy a set of mixed commutation relations among themselves. Identifying x and p with the coordinates and derivatives of the D-brane world volume, we find a new type of noncommutative space which is very different from those associated with a constant B field background.

Noncommutative Dirac–Born–Infeld action for D-brane

We derive the noncommutative Dirac–Born–Infeld action for the D-brane, which governs dynamics of D-brane with a NS-NS B-field in the low energy regime. Depending on some details of the path integral prescriptions, both ordinary Dirac–Born–Infeld action and noncommutative one can be obtained by evaluating the same Polyakov string path integral for the open string ending on the D-brane. Thus, it establishes the equivalence of the noncommutative Dirac–Born–Infeld action and the ordinary one.

Worldvolume uncertainty relations for D-branes

By quantizing an open string ending on a D-brane in a nontrivial supergravity background, we argue that there is a new kind of uncertainty relation on a D-brane worldvolume. Furthermore, we fix the form of the uncertainty relations and their dependence on the string coupling constant by requiring them to be consistent with various string theory and M theory dualities. In this way we find a web of uncertainties of spacetime for all kinds of brane probes, including fundamental strings, D-branes of all dimensions as well as M theory membranes and fivebranes.

Matrix model for Dirichlet open string

We discuss the open string ending on D p-branes in IKKT framework. First we determine the boundary conditions of Green-Schwarz superstring which are consistent with supersymmetry and κ-symmetry. We point out some subtleties arising from taking the Schild gauge and show that in this gauge the system incorporates the limited dimensional D p-branes ( p=3,7). The matrix regularization for the Dirichlet open string is given by gauge group SO( N). When p=3, the matrix model becomes the dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory.

Temporal-gauge string field with open strings

A string field theory including open string fields is constructed in the temporal gauge. It consists of string interaction vertices similar to the light-cone gauge string field theory. A slight modification of the definition of the time coordinate is needed because of the existence of the open string end points.

Cosmic strings with curvature corrections

A generic model of string described by a Lagrangian density that depends on the extrinsic curvature of the string worldsheet is studied. Using a system of coordinates adapted to the string world sheet the equation of motion and the energy-momentum tensor are derived for strings evolving in curved spacetime. We find that the curvature corrections may change the relation between the string energy density and the tension. It can also introduce heat propagation along the string. We also find for the Polyakov as well as Nambu strings with a topological term that the open string end points can travel with a speed less than the velocity of light.

Twist symmetry and open-string Wilson lines

The Möbius amplitude plays an important role in open-string theories, since it determines which sectors of a given model consist of unoriented open strings. It also fixes the Chan-Paton representations of all their states, according to the behavior under the interchange of the ends of open strings (“twist”). In this paper we discuss the role played by conventional Wilson lines in Chan-Paton symmetry breaking, and we show that the presence of an extended symmetry algebra allows, in general, a number of choices for the behavior of massive states under twist. This freedom may be ascribed to additional discrete Wilson lines, and yields consistent modifications of the group assignments, that are illustrated in a number of examples.

Precession of classical spin and spin-orbit splitting

We describe classical spinning particles in external fields. This formalism is extended to spinning particles localized at the ends of open Nambu strings. We consider the relations between the frequencies of spin precession and the energy of spin-orbit splitting.

Group theory from “quarks” at the ends of strings

We add D fermionic variables to the ends of open strings, generating the combinatoric and group theory factors of SO(2 [ D/2] ). Thus 10 variables give SO(32). The results are illustrated by a one-loop calculation, giving the partition function of the theory. We discuss boundary conditions, and the modifications of the Feynman rules needed for obtaining the groups U(2 [ D 2 ] ) and USp(2 [ D 2 ] ) .