Narrow Results

The fusion rings of the Wess–Zumino–Witten models are re-examined. Attention is drawn to the difference between fusion rings over ℤ (which are often of greater importance in applications) and fusion algebras over ℂ. Complete proofs are given by characterizing the fusion algebras (over ℂ) of the SU(r+1) and Sp(2r) models in terms of the fusion potentials, and it is shown that the analagous potentials cannot describe the fusion algebras of the other models. This explains why no other representation-theoretic fusion potentials have been found.

Instead, explicit generators are then constructed for general WZW fusion rings (over ℤ). The Jacobi–Trudy identity and its Sp(2r) analogue are used to derive the known fusion potentials. This formalism is then extended to the WZW models over the spin groups of odd rank, and explicit presentations of the corresponding fusion rings are given. The analogues of the Jacobi–Trudy identity for the spinor representations (for all ranks) are derived for this purpose, and may be of independent interest.

We investigate D-branes with maximal symmetry on general group manifolds in terms of boundary states and effective actions. We show that in large k limit boundary states with a suitable Wilson line form boundary states of the other types of D-branes, extending the known fact in SU(2) case. We also show that fluctuation mass spectrum around D-brane solutions of the effective action agrees with that of boundary CFT in large k limit.

For the D-branes on the SL(2,R) WZW model we present a particular choice of outer automorphism for the gluing condition of currents that leads to a special AdS₂ brane configuration. This configuration is shown to be a static solution in the cylindrical coordinates, and a nonstatic solution in the Poincaré coordinates to the nonlinear equation of motion for the Dirac–Born–Infeld action of a D-string. The generalization of it gives a family of nonstatic AdS₂ brane solutions. They are demonstrated to transform to each other under the isometry group of AdS₃ space–time.

We find nonsupersymmetric and supersymmetric solutions of D3 brane configuration in the background of pp-wave obtained as a Penrose limit of AdS₅ × S⁵.

In this paper, we study the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in the presence of a magnetic field. We outline the analogy between cyclic and noncommutative symmetries and demonstrate the point-splitting prescription to explain some of the unusual ir phenomena observed in a noncommutative field theory.

In this paper we study the noncommutativity of a moving membrane with background fields. The open string variables are analyzed. Some scaling limits are studied. The equivalence of the magnetic and electric noncommutativities is investigated. The conditions for equivalence of noncommutativity of the T-dual theory in the rest frame and noncommutativity of the original theory in the moving frame are obtained.

The Higgs sector of the low-energy physics of n coincident D-branes contains the necessary elements for constructing noncommutative manifolds. The coordinates orthogonal to the coincident branes, as well as their conjugate momenta, take values in the Lie algebra of the gauge group living inside the brane stack. In the limit when n→∞ (and in the absence of orientifolds), this is the unitary Lie algebra u(∞). Placing a smooth manifold orthogonally to the stack of coincident D-branes, one can construct a noncommutative C^⋆-algebra that provides a natural definition of a noncommutative partner for the manifold .

This is a brief review of Refs. 1 and 2. We study the dynamics of D0-brane falling into the Lorentzian two-dimensional black hole (2D BH), typically arising in the near-horizon limit of non-extremal NS5-brane background, by the methods of conformal field theory. We propose the exact boundary state describing the infalling D0-brane by carefully carrying out the Wick rotation from the known D1-brane solution. We evaluate the closed string radiation from the infalling brane. A thermal-like behavior at the Hawking temperature is observed in the outgoing radiation. On the other hand, it is remarkable to find the incoming radiation absorbed by the black hole effectively showing the Hagedorn-like behavior with precise α′-correction. We confirm this feature by exactly analyzing the imaginary part of cylinder amplitudes, as well as the saddle point approximation. The radiation rate curiously depends on the level k of SL(2)/U(1) supercoset, suggesting the "black hole/string phase transition" at k = 1 (k = 3 for the bosonic coset) discussed recently.

We propose a full-fledged open string framework that seems suited to study the black hole information paradox. We set up a configuration to compute the scattering amplitude of a IIB open string around a D5-brane. The D5-brane is situated at the origin of a transverse D3-brane. A string perturbation theory is employed where the geometry of the D5-brane is treated as a potential. We reason that the setup is capable of reconciling the unitary evolution of states and information loss that is measured by an observer on the D3 brane. With the configurations of these kinds, the information loss is an apparent phenomenon: it is just a manifestation of the fact that the D3-observer does not have access to the "hair" of the D5 black brane.

According to the open-closed mirror symmetry and generalized Gel'fand–Kapranov–Zelerinski (GKZ) system, we calculate off-shell D-brane/F-theory effective superpotentials of four compact Calabi–Yau (CY) manifolds by integrating special periods of subsystem, and extracting the open Ooguri–Vafa invariants from the expansion of off-shell D-brane superpotentials.

We calculate the D-brane superpotentials for two Calabi–Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials 𝒲_GVW of the dual F-theory compactification on the relevant Calabi–Yau fourfolds in the weak decoupling limit. We also compute the Ooguri–Vafa invariants from A-model expansion with mirror symmetry, which are related to the open Gromov–Witten invariants.

Following the work of David Fairlie and his collaborators, we discuss the geometry of the equations of motion for the companion Lagrangian. This arises while we attempt to construct the field theoretic Lagrangians for strings and branes. These equations are related to generalized Bateman equations. Interestingly, an inhomogeneous form of these equations are related to what Dubrovin and Novikov called equations of the hydrodynamic type. We translate this set of equations into (Nambu)–Poisson equations and formulate the Lax representation of these systems. We deform all this set of equations by the Moyal product. We also present the Lax pair of the Moyal deformed systems for some special cases.

We study dynamics of a D3-brane propagating in the vicinity of k coincident NS5 branes. We show that when g_s is small, there exists a regime in which dynamics of the D-brane is governed by Dirac–Born–Infeld action while higher order derivative in the expansion cannot be neglected. This leads to a restriction on how fast scalar field may roll. We analyze the motion of a rolling scalar field in this regime, and extend the analysis to cosmological systems obtained by coupling this type of field theory to four-dimensional gravity. It also leads to some FRW cosmologies, some of which are related to those obtained with tachyon matter.

We investigate D-branes in the Nappi–Witten model. Classically symmetric D-branes are classified by the (twisted) conjugacy classes of the Nappi–Witten group, which specify the geometry of the corresponding D-branes. Quantum description of the D-branes is given by boundary states, and we need one-point functions of closed strings to construct the boundary states. We compute the one-point functions solving conformal bootstrap constraints, and check that the classical limit of the boundary states reproduces the geometry of D-branes.

We explore the geometry of superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for NSR strings, free of picture-changing complications. The sigma-model generating functional is constructed by the integration over the bosonic and fermionic moduli, corresponding to insertions of the vertex operators in scattering amplitudes. While the integration over the supermoduli leads to the standard picture-changing insertions, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c fermionic ghosts with the ghost number -1. Important example of the b-c ghost pictures involves the vertex operators in integrated and unintegrated forms. We obtain the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR theory contain the global singularities, leading to the phenomenon of ghost-matter mixing and the appearance of nonperturbative D-brane creation operators.

Atick and Witten have proposed the Hagedorn transition of closed strings via condensation of 'winding tachyon'. But we have not known the stable minimum of this tachyon potential yet. On the other hand, we have previously shown that a phase transition occurs near the Hagedorn temperature and D9-brane– -brane pairs become stable. We present a conjecture that D9-brane– -brane pairs are created by the Hagedorn transition of closed strings. We will show some circumstantial evidences for this conjecture.

We report on the boundary state of superstring in the open string channel, which describes the superconformal field theory of open string emission and absorption by D-brane.

In this poster, we study the boundary states of the three-state Potts model coupled to two dimensional gravity, which we call Z₃ extended minimal string. We find that two different boundary states of this model can be identified with a shift of the boundary cosmological constant. We also point out that the boundary states are classified with respect to the symmetry of the theory. This presentation is based on Ref. 1 to appear soon.

We briefly review a tunneling picture of rotating D3-brane solutions. By applying the "double Wick rotation" to the Lorentzian solutions, we construct Euclidean solutions. The solutions are composed of dual giant gravitons and spike D3-brane solutions, and their classical actions reproduce expectation values of the k-th symmetric Wilson loops as well as correlation functions of dual giant graviton operators as expected.

From BFSS matrix theory considerations, it is expected that a single D_p+2-brane action can be obtained from ND_p-brane action in large N limit. We examine and confirm this expectation by working out the details of DBI and Chern–Simons terms of D_p+2-brane action from D_p-brane action. We show that the same relation works for non-BPS, as well as BPS branes.