World-sheet Boundary Research Articles

Rolling tachyon in Anti-de Sitter space-time

We study the decay of the unstable D-particle in three-dimensional anti-de Sitter space-time using worldsheet boundary conformal field theory methods. We test the open string completeness conjecture in a background for which the phase space available is only field-theoretic. This could present a serious challenge to the claim. We compute the emission of closed strings in the AdS(3) x S^3 x T^4 background from the knowledge of the exact corresponding boundary state we construct. We show that the energy stored in the brane is mainly converted into very excited long strings. The energy stored in short strings and in open string pair production is much smaller and finite for any value of the string coupling. We find no "missing energy" problem. We compare our results to those obtained for a decay in flat space-time and to a background in the presence of a linear dilaton. Some remarks on holographic aspects of the problem are made.

Normal ordering and boundary conditions for fermionic string coordinates

Abstract We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy–momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.

Abelian and Non-Abelian Branes in WZW Models and Gerbes

We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet boundary to brane submanifolds in the target group. Such submanifolds are equipped with an additional geometric structure that is summarized in the notion of a gerbe module and includes a twisted Chan-Paton gauge field. Using the geometric approach, we present a complete classification of the branes that conserve the diagonal current-algebra symmetry in the WZW models with simple, compact but not necessarily simply connected target groups. Such symmetric branes are supported by a discrete series of conjugacy classes in the target group and may carry Abelian or non-Abelian twisted gauge fields. The latter situation occurs for the conjugacy classes with fundamental group ℤ2×ℤ2 in SO(4n)/ℤ2. The branes supported by such conjugacy classes have to be equipped with a projectively flat twisted U(2) gauge field in one of the two possible WZW models differing by discrete torsion. We show how the geometric description of branes leads to explicit formulae for the boundary partition functions and boundary operator product coefficients in the WZW models with non-simply connected target groups.

Exact Solutions in SFT and Marginal Deformation in BCFT

In this note we will study solution of open bosonic string field theory based on action of operators from chiral algebra of boundary conformal field theory on identity element of string field theory star algebra. We will demonstrate that the string field theory action for fluctuation fields around this classical solution can be mapped to the string field theory action defined through the new boundary conformal field theory that arises from the original one through the marginal deformation inserted on the world-sheet boundary.

Supersymmetric Born-Infeld from the Pure Spinor Formalism of the Open Superstring

Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N=1 D=10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions.

Wilson Loops, D-Branes, and Reparametrization Path-Integrals

We study path-integrals over reparametrizations of the world-sheet boundary. Such integrals arise when string propagates between fixed space-time contours. In gauge/string duality they are needed to describe gauge theory Wilson loops. We show that (1) in AdS/CFT, the integral is well defined and gives a finite 1-loop correction to the Wilson loop; (2) in critical string theory, the integral is UV divergent, and fixed contour amplitudes are off shell. In the second case, we show that the divergences can be removed by renormalizing the contour. We calculate the 2-loop contour beta-function and explain how it is related to the D0-brane effective action. We also apply this method to compute the first alpha' correction to the effective action of higher dimensional branes.

Closed strings from nothing

We study the physics of open strings in bosonic and type-II string theories in the presence of unstable D-branes. When the potential energy of the open string tachyon is at its minimum, Sen has argued that only closed strings remain in the perturbative spectrum. We explore the scenario of Yi and of Bergman, Hori, and Yi, who argue that the open string degrees of freedom are strongly coupled and disappear through confinement. We discuss arguments using open string field theory and world sheet boundary renormalization group flows, which seem to indicate otherwise. We then describe a solitonic excitation of the open string tachyon and gauge field with the charge and tension of a fundamental closed string. This requires a double scaling limit where the tachyon is taken to its minimal value and the electric field is taken to its maximum value. The resulting flux tube has an unconstrained spatial profile; and for large fundamental string charge it appears to have light, weakly coupled open strings existing in the core. We argue that the flux tube acquires a size of order ${\ensuremath{\alpha}}^{\ensuremath{'}}$ through sigma model and string coupling effects, and that confinement effects make the light degrees of freedom heavy and strongly interacting.

HAMILTONIAN FORMULATION OF OPEN WZW STRINGS

Using a Hamiltonian approach, we construct the classical and quantum theory of open WZW strings on a strip. (These are the strings which end on WZW branes.) The development involves non-Abelian generalized Dirichlet images in an essential way. At the classical level, we find a new non-commutative geometry in which the equal-time coordinate brackets are non-zero at the world-sheet boundary, and the result is an intrinsically non-Abelian effect which vanishes in the Abelian limit. Using the classical theory as a guide to the quantum theory, we also find the operator algebra and the analogue of the Knizhnik–Zamolodchikov equations for the conformal field theory of open WZW strings.

Open strings, holography and stochastic processes

We use the correspondence between string states and local operators on the world-sheet boundary defined by vertex operators in open string theory to put in correspondence, holographically, the bosonic open string with the large N limit of a mechanical system living on the world-sheet boundary. We give a natural interpretation of this system in terms of a one-dimensional stochastic process and show that the correspondence takes the form of a map between two conformal field theories with central charge c=24 and c=1.

Projections in string theory and boundary states for Gepner models

In string theory various projections have to be imposed to ensure supersymmetry. We study the consequences of these projections in the presence of world-sheet boundaries. A-type boundary conditions come in several classes; only boundary fields that do not change the class preserve supersymmetry. Our analysis takes in particular properly into account the resolution of fixed points under the projections. Thus, e.g., the compositeness of some previously considered boundary states of Gepner models follows from chiral properties of the projections. Our arguments are model independent; in particular, integrality of all annulus coefficients is ensured by model independent arguments.

Superstring scattering from D-branes bound states

We derive fully covariant expressions for disk scattering amplitudes of any two massless closed strings in which mixed Neumann and Dirichlet world-sheet boundary conditions are included. From the two-point amplitudes, we derive the long range background fields and verify that they correspond to D$p$-brane bound state. Also, from the scattering amplitudes, we calculate the linear coupling of closed string fields to D-brane world-volume and show that they are consistent with Born-Infeld and Chern-Simons actions in the presence of a background field.

Symmetry breaking at enhanced symmetry points

The influence of world-sheet boundary condensates on the toroidal compactification of bosonic string theories is considered. At the special points in the moduli space at which the closed-string theory possesses an enhanced unbroken G × G symmetry (where G is a semi-simple product of simply laced groups) a scalar boundary condensate parameterizes the coset G × G/ G. Fluctuations around this background define an open-string generalization of the corresponding chiral non-linear sigma model. Tree-level scattering amplitudes of on-shell massless states (‘pions’) reduce to the amplitudes of the principal chiral model for the group G in the low-energy limit. Furthermore, the condition for the vanishing of the renormalization group beta function at one loop results in the familiar equation of motion for that model. The quantum corrections to the open-string theory generate a mixing of open and closed strings so that the coset-space pions mix with the closed-string G × G gauge fields, resulting in a Higgs-like breakdown of the symmetry to the diagonal G group. The case of non-oriented strings is also discussed.

A gas of D-instantons

A D-instanton is a space-time event associated with world-sheet boundaries that contributes non-perturbative effects of order e −const. κ to closed-string amplitudes. Some properties of a gas of D-instantons are discussed in this paper.

Multi-boundary effects in Dirichlet string theory

String amplitudes with an arbitrary number of world-sheet boundaries on which the coordinates satisfy Dirichlet boundary conditions are analysed in a path integral framework. Special attention is paid to the novel divergences associated with such conditions. Certain helicity amplitudes involving massless closed-string states are free of such divergences to all orders in perturbation theory and their behavior can be analysed unambiguously. The high-energy fixed-angle behavior of these amplitudes is discussed in the presence of one or two boundaries and the asymptotic behavior of the amplitudes is shown to be power behaved.

The insertion of boundaries in world-sheets

This paper considers the operator that inserts a boundary in a string world-sheet on which the string coordinates satisfy either Neumann or constant Dirichlet boundary conditions. With an arbitrary open-string state attached to the boundary, this describes the vertex coupling an open string to a closed string (the “open-closed string vertex”). A boundary with no open strings attached can be viewed as a vacuum correction to closed-string theory. This factories into two open-closed string vertices joined together by an open-string propagator. BRST-invariant open-closed string vertices of the Neumann and Dirichlet theories are constructed in a “light-cone-like” frame (familiar from some formulations of covariant string field theory) as well as the “vertex operator” frame (in which a general open-string state is represented by a vertex operator attached to the world-sheet boundary). The vertices of the Neumann and Dirichlet theories are related to each other by space-time duality. The insertion of a closed Dirichlet boundary may be expressed in the light-cone-like gauge as an interaction vertex that acts at a fixed “time” and generates an explicit mass term connecting two arbitrary closed-string states. Some examples of how the presence of such boundaries modifies amplitudes for low-lying states are presented.

Summing over world-sheet boundaries

The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the embedding coordinates. A light-cone parameterization of such boundaries is also discussed.

Classical open string models in four-dimensional Minkowski spacetime.

Classical bosonic open string models in four-dimensinal Minkowski spacetime are discussed. Special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider Lagrangians that can depend on second order derivatives of world sheet coordinates. A revised interpretation of the variational problem for such string theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary problem for minimal surface is examined. Following the treatment of this model in the geometric approach, we obtain that classical open string states correspond to solutions of a complex Liouville equation. In contrast with the Nambu-Goto case, the Liouville potential is finite and constant at world sheet boundaries. The phase part of the potential defines topological sectors of solutions.

The influence of world-sheet boundaries on critical closed string theory

This paper considers interactions between closed strings and open strings satisfying either Neumann or constant (point-like) Dirichlet boundary conditions in a BRST formalism in the critical dimension. With Neumann conditions this reproduces the well-known stringy version of the Higgs mechanism. With Dirichlet conditions the open-string states correspond to either auxiliary or Lagrange multiplier target-space fields and their coupling to the closed-string sector leads to constraints on the closed-string spectrum.

Temperature dependence of string theory in the presence of world-sheet boundaries

The effect of world-sheet boundaries on the temperature-dependence of bosonic string theory is studied to first order in string perturbation theory. The high-temperature behaviour of a theory with Dirichlet boundary conditions has features suggestive of the high-temperature limit of the confining phase of large- n SU ( n) Yang-Mills theory, recently discussed by Polchinski.