String Vertex Research Articles

Comments on Superstring Interactions in a Plane-Wave Background

The three string vertex for Type IIB superstrings in a maximally supersymmetric plane-wave background is investigated. Specifically, we derive a factorization theorem for the Neumann coefficients that generalizes a flat-space result that was obtained some 20 years ago. The resulting formula is used to explore the leading large mu asymptotic behavior, which is relevant for comparison with dual gauge theory results.

Computing in string field theory using the Moyal star product

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as a closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.

Chiral splitting and world-sheet gravitinos in higher-derivative string amplitudes

We report on progress made in the construction of higher-derivative superinvariants for type-II theories in ten dimensions. The string amplitude calculations required for this analysis exhibit interesting features which have received little attention in the literature so far. We discuss two examples from a forthcoming publication: the construction of the (HNS)2 R3 terms and the fermionic completion of the ϵϵR4 terms. We show that a correct answer requires very careful treatment of the chiral splitting theorem, implies unexpected new relations between fermionic correlators, and most interestingly, necessitates the use of world-sheet gravitino zero modes in the string vertex operators. In addition we compare the relation of our results to the predictions of the linear scalar superfield of the type-IIB theory.

Sewing string tree vertices with ghosts

It is shown how to sew string vertices with ghosts at tree level in order to produce new tree vertices using the Group Theoretic approach to String Theory. It is then verified the BRST invariance of the sewn vertex and shown that it has the correct ghost number.

Open strings in simple current orbifolds

We study A a b branes and open strings in a large class of orbifold backgrounds using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z 2 orbifolds of the SU(2) WZW model and in the D-series of unitary minimal models considered previously by Runkel.

Siegel Gauge in Vacuum String Field Theory

We study the star algebra of ghost sector in vacuum string field theory (VSFT). We show that the star product of two states in the Siegel gauge is BRST exact if we take the BRST charge to be the one found in hep-th/0108150, and the BRST exact states are nil factors in the star algebra. By introducing a new star product defined on the states in the Siegel gauge, the equation of motion of VSFT is characterized as the projection condition with respect to this new product. We also comment on the comma form of string vertex in the ghost sector.

Comments on D-branes in AdS3

We study D-branes that preserve a diagonal SL(2) affine Lie algebra in string theory on AdS 3. We find three classes of solutions, corresponding to the following representations of SL(2): (1) degenerate, finite-dimensional representations with half integer spin, (2) principal continuous series, (3) principal discrete series. We solve the bootstrap equations for the vacuum wave functions and discuss the corresponding open string spectrum. We argue that from the point of view of the AdS/CFT correspondence, the above D-branes introduce boundaries with conformal boundary conditions into the two-dimensional spacetime. Open string vertex operators correspond to boundary perturbations. We also comment on the geometric interpretation of the branes.

Comma vertex and string field algebra

We study the matter part of the algebra of open string fields using the 3-string vertex over the sliver state, which we call ``comma vertex''. By generalizing this comma vertex to the $N$-string overlap, we obtain a closed form of the Neumann coefficients in the $N$-string vertex and discuss its relation to the oscillator representation of wedge states.

Open string fields as matrices

We present a new representation of the string vertices of the cubic open string field theory. By using this three-string vertex, we attempt to identify open string fields as huge-sized matrices by following Witten's idea. By using these huge matrices, we obtain some results about the construction of partial isometries in the algebra of open string fields.

On superpotentials for D-branes in Gepner models

A large class of D-branes in Calabi-Yau spaces can be constructed at the Gepner points using the techniques of boundary conformal field theory. In this note we develop methods that allow to compute open string amplitudes for such D-branes. In particular, we present explicit formulas for the products of open string vertex operators of untwisted A-type branes. As an application we show that the boundary theories of the quintic associated with the special Lagrangian submanifolds Im \omega_i z_i = 0 where \omega_i^5=1 possess no continuous moduli.

Fundamental strings in D–D brane systems

We study conformal field theory correlation functions relevant for string diagrams with open strings that stretch between several parallel branes of different dimensions. In the framework of conformal field theory, they involve boundary condition changing twist fields which intertwine between Neumann and Dirichlet conditions. A Knizhnik–Zamolodchikov-like differential equation for correlators of such boundary twist fields and ordinary string vertex operators is derived, and explicit integral formulas for its solutions are provided.

The geometry of WZW branes

The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string vertex operators. In the limit of large level, we find branes whose world volume is a regular conjugacy class or, in the case of symmetry breaking boundary conditions, a ‘twined’ version thereof. In particular, in this limit one recovers the commutative algebra of functions over the brane world volume, and open strings connecting different branes disappear. At finite level, the branes get smeared out, yet their approximate localization at (twined) conjugacy classes can be detected unambiguously. It is also established that in any rational conformal field theory the structure constants of the algebra of boundary operators coincide with specific entries of fusing matrices.

D-branes and deformation quantization

In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume algebras from the operator product expansions of open string vertex operators. For branes in a flat background with constant non-vanishing B-field, the operator products are computed perturbatively to all orders in the field strength. The resulting series coincides with Kontsevich's presentation of the Moyal product. After extending these considerations to fermionic fields we conclude with some remarks on the generalization of our approach to curved backgrounds.

An affine string vertex operator construction at an arbitrary level

An affine vertex operator construction at an arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is manifestly physical in the sense of string theory, i.e., the vertex operators are functions of Del Giudice–Di Vecchia–Fubini (DFF) “oscillators” and the Lorentz generators, both of which commute with the Virasoro constraints. We therefore obtain explicit representations of affine highest weight modules in terms of physical (DDF) string states. This opens new perspectives on the representation theory of affine Kac–Moody algebras, especially in view of the simultaneous treatment of infinitely many affine highest weight representations of arbitrary level within a single state space as required for the study of hyperbolic Kac–Moody algebras. A novel interpretation of the affine Weyl group as the “dimensional null reduction” of the corresponding hyperbolic Weyl group is given, which follows upon re-expression of the affine Weyl translations as Lorentz boosts.

Fundamental Strings and D-Strings in the IIB Matrix Model

The matrix model for IIB superstring proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya is investigated. Consideration of planar and non-planar diagrams suggests that large-N perturbative expansion is consistent with the double scaling limit proposed by the above authors. We write down a Wilson loop that can be interpreted as a fundamental string vertex operator. The one-point tadpole in the presence of a D-string has the right form and this can be viewed as a matrix model derivation of the boundary conditions that define a D-string. We also argue that if worldsheet coordinates σ and τ are introduced to the fundamental string, then the conjugate variable d/dσ and d/dτ can be interpreted as the D-string worldsheet coordinates. In this way the SL (2Z) duality group of the IIB superstring becomes identified with the symplectic group acting on (p,q).

String winding modes from charge non-conservation in compact Chern-Simons theory

In this letter we show how string winding modes can be constructed using topological membranes. We use the fact that monopole-instantons in compact topologically massive gauge theory lead to charge non-conservation inside the membrane which, in turn, enables us to construct string vertex operators with different left and right momenta. The amount of charge non-conservation inside the membrane is interpreted as giving the momentum associated with the string winding mode and is shown to match precisely the full mass spectrum of compactified string theory. We also argue that if heterotic strings are described by topological membranes, then all space-time dimensions must be compact.

New moduli spaces from string background independence consistency conditions

In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the consistency conditions associated to the commutator of two deformations are implemented by virtue of the existence of moduli spaces of punctured surfaces with two special punctures. The spaces are antisymmetric under the exchange of the special punctures, and satisfy recursion relations relating them to moduli spaces with one special puncture and to string vertices. We develop the theory of moduli spaces of surfaces with arbitrary number of special punctures and indicate their relevance to the construction of a string field theory that makes no reference to a conformal background. Our results also imply a partial antibracket cohomology theorem for the string action.

BRST properties of spin fields

For the closed superstring, spin fields and bi-spinor states are defined directly in four spacetime dimensions, in van der Waerden notation (dotted and undotted indices). Explicit operator product expansions are given, including those for the internal superconformal field theory, which are consistent with locality and BRST invariance for the string vertices. The most general BRST picture changing for these fields is computed. A covariant notation for the spin decomposition of these states is developed in which non-vanishing polarizations are selected automatically. The kinematics of the three-gluon dual model amplitude in both the Neveu-Schwarz and Ramond sectors in the Lorentz gauges is calculated and contrasted. Modular invariance and enhanced gauge symmetry of four-dimensional models incorporating these states is described.

Off-shell closed string amplitudes: Towards a computation of the tachyon potential

We derive an explicit formula for the evaluation of the classical closed string action for any off-shell string field, and for the calculation of arbitrary off-shell amplitudes. The formulae require a parametrization, in terms of some moduli space coordinates, of the family of local coordinates needed to insert the off-shell states on Riemann surfaces. We discuss in detail the evaluation of the tachyon potential as a power series in the tachyon field. The expansion coefficients in this series are shown to be geometrical invariants of Strebel quadratic differentials whose variational properties imply that closed string polyhedra, among all possible choices of string vertices, yield a tachyon potential which is as small as possible order by order in the string coupling constant. Our discussion emphasizes the geometrical meaning of off-shell amplitudes.

THE INVARIANT CHARGES OF THE NAMBU–GOTO THEORY: NON-ADDITIVE COMPOSITION LAWS

With continuity as the essential ingredient, insight is gained into the existence, number and structure of algebraic relations among the invariant charges corresponding to the three branches of a string vertex in the classical Nambu–Goto theory. C-number and algebraic aspects of these relations are discussed.