Disk Amplitudes Research Articles

Fermion representation of the rolling tachyon boundary conformal field theory

A free fermion representation of the rolling tachyon boundary conformal field theory is constructed. The representation is used to obtain an explicit, compact, exact expression for the boundary state. We use the boundary state to compute the disc and cylinder amplitudes for the half-S-brane.

Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A-infinity relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

Formula omitted]-Trek III: the search for Ramond–Ramond couplings

We give a detailed discussion of the disk amplitudes with one closed string insertion, which we used to construct the supergravity couplings of noncommutative D-branes to the RR potentials, given in hep-th/0104139. We prove the inclusion of Elliott's formula, the integer-valued modification of the noncommutative Chern character, to all orders in the gauge field. We also give a detailed comparison between the form of the result in which Elliott's formula is manifest, and the form expressed in Matrix model variables.

Supergravity couplings of noncommutative D-branes

We discuss the supergravity couplings of noncommutative D-branes by considering the disk amplitudes with one closed string insertion. The result confirms a recent proposal for the general form of the noncommutative Yang–Mills operators coupling to the massless closed string modes. The construction involves smearing Yang–Mills field variables along an open Wilson line. For multiple D-branes interacting with background supergravity fields, this prescription reduces, in the B=0 limit, to the “symmetrized trace” prescription, and the supergravity fields are seen to be functionals of the nonabelian scalar fields on the branes.

D-branes in singular Calabi–Yau n-fold and N=2 Liouville theory

Making use of the N=2 Liouville theory and world-sheet techniques, we study the properties of D-branes wrapped around vanishing SUSY cycles of singular Calabi–Yau n-folds (n=2,3,4). After constructing boundary states describing the wrapped branes, we evaluate the disc amplitudes corresponding to the periods of SUSY cycles. We use the old technique of KPZ scaling in Liouville theory and derive holomorphicity and scaling behavior of vanishing cycles which are in agreement with geometrical considerations. We also discuss the open string Witten index using the N=2 Liouville theory and obtain the intersection numbers among SUSY cycles which also agree with geometrical expectation.

Stable massive states in(1+1)-dimensional noncommutative open string theory

We study the case of open string theory on a D1-brane in a critical electric field. It was argued by Klebanov and Maldacena that the massless open string modes of this theory decouple from the massive modes, corresponding to a decoupling of the U(1) degrees of freedom in the $\mathrm{U}(N)$ gauge theory dual. To provide further support for the decoupling, we present several examples of open string disk amplitudes. Because of the decoupling, many of the massive open string states are stable, indicating the presence of a number of correspondingly stable states in the gauge theory. We provide a lengthy list of these stable states. However, when the theory is compactified in the spatial direction of the electric field, we demonstrate that such sufficiently massive states may decay into wound-closed strings.

Splitting of Heterogeneous Boundaries in a System of the Tricritical Ising Model Coupled to 2-Dim Gravity

We study disk amplitudes whose boundaries have heterogeneous matter states in a system of $(4,5)$ conformal matter coupled to 2-dim gravity. They are analysed by using the 3-matrix chain model in the large $N$ limit. Each of the boundaries is composed of two or three parts with distinct matter states. From the obtained amplitudes, it turns out that each heterogeneous boundary loop splits into several loops and we can observe properties in the splitting phenomena that are common to each of them. We also discuss the relation to boundary operators.

Stretched strings in noncommutative field theory

Motivated by recent discussions of IR/UV mixing in noncommutative field theories, we perform a detailed analysis of the non-planar amplitudes of the bosonic open string in the presence of an external B-field at the one-loop level. We carefully isolate, at the string theory level, the contribution which is responsible for the IR/UV behavior in the field theory limit. We show that it is a pure open string effect by deriving it from the factorization of the one-loop amplitude into the disk amplitudes of intermediate open string insertions. We suggest that it is natural to understand IR/UV mixing as the creation of intermediate ``stretched strings''.

Disk amplitudes in the topological A-model on Calabi-Yau spaces and Fano manifolds

We study topological A-model disk amplitudes with Calabi-Yau target spaces by mirror symmetries. This allows us to calculate holomorphic instantons of Riemann surfaces with boundaries that are mapped into SUSY cycles in Calabi-Yau d-folds. Also we analyse disk amplitudes in Fano manifold cases by considering fusion relations between A-model operators.

Topological Sector of Disk Amplitudes on Calabi-Yau Spaces and Fano Manifolds

Topological Sector of Disk Amplitudes on Calabi-Yau Spaces and Fano Manifolds

Interaction of boundaries with heterogeneous matter states in matrix models

We study disk amplitudes whose boundary conditions on matter configurations are not restricted to homogeneous ones. They are examined in the two-matrix model as well as in the three-matrix model for the case of the tricritical Ising model. Comparing these amplitudes, we demonstrate relations between degrees of freedom of matter states in the two models. We also show that they have a simple geometrical interpretation in terms of interactions of the boundaries. It plays an important role that two parts of a boundary with different matter states stick to each other. We also find two closed sets of Schwinger-Dyson equations which determine disk amplitudes in the three-matrix model.

Unoriented Open-Closed String Field Theory

The string field theory for unoriented open-closed string mixed system is constructed up to quadratic order based on the joining-splitting type vertices. The gauge invariance with closed string transformation parameter is proved. The infinity cancellation mechanism between disk and projective plane amplitudes plays an essential role for the gauge invariance of the theory.

The Relation between Mixed Boundary States in Two- and Three-Matrix Models

We discuss the relation among some disk amplitudes with non-trivial boundary conditions in two-dimensional quantum gravity. They are obtained by the two-matrix model as well as the three-matirx model for the case of the tricritical Ising model. We examine them for simple spin configurations, and find that a finite number of insertions of the different spin states cannot be observed in the continumm limit. We also find a closed set of eight Schwinger-Dyson equations which determines the disk amplitudes in the three-matrix model.

CRITICAL BEHAVIOR IN c=1 MATRIX MODEL WITH BRANCHING INTERACTIONS

In order to understand the phase structure of d>1 strings we investigate the c=1 matrix model with g′(tr M(t)2)2 interaction which is the simplest approximation of the large-N reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary c=1 gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase, and compute the disk and cylinder amplitudes in the phases (i) and (iii). Further we also analyze the model with slightly generalized [Formula: see text][Formula: see text] interaction. As a result the multi-critical versions of the phase (ii) are found.

Planar duality in the discrete series

The models of the discrete series of Belavin, Polyakov and Zamolodchikov may be generalized by allowing for suitable open-string sectors. The resulting open-string disk amplitudes have planar duality and proper factorization in the presence of a global internal Chan-Paton symmetry.