Volume 42, Issue 7, July 2001
 SPECIAL ISSUE: STRINGS, BRANES, AND MTHEORY

 STRINGS AND DBRANES

The Hagedorn transition in noncommutative open string theory
View Description Hide DescriptionThe Hagedorn transition in noncommutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five space–time dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the Dbrane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated from the bound state.

Noncommutative tachyons and Ktheory
View Description Hide DescriptionWe show that the relation between Dbranes and noncommutative tachyons leads very naturally to the relation between Dbranes and Ktheory. We also discuss some relations between Dbranes and Khomology, provide a noncommutative generalization of the ABS construction, and give a simple physical interpretation of Bott periodicity. In addition, a framework for constructing Neveu–Schwarz fivebranes as noncommutative solitons is proposed.

NonAbelian Dbranes and noncommutative geometry
View Description Hide DescriptionWe discuss the nonAbelian worldvolume action which governs the dynamics of coincident branes. In this theory, the branes’ transverse displacements are described by matrixvalued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which branes may be polarized into a noncommutative geometry by external fields. Another example is the appearance of noncommutative geometries in the description of intersecting Dbranes of differing dimensions, such as Dstrings ending on a D3 or D5brane. We also describe the related physics of giant gravitons.

Superstrings and topological strings at large N
View Description Hide DescriptionWe embed the large N Chern–Simons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with supersymmetry in four dimensions and superstrings propagating on noncompact Calabi–Yau manifolds with certain fluxes turned on. We also show that in a particular limit of the gauge theory system, certain superpotential terms in the system (including deformations if spacetime is noncommutative) are captured to all orders in by the amplitudes of noncritical bosonic strings propagating on a circle with selfdual radius. We also consider Dbrane/antiDbrane system wrapped over vanishing cycles of compact Calabi–Yau manifolds and argue that at large N they induce a shift in the background to a topologically distinct Calabi–Yau, which we identify as the ground state system of the brane/antibrane system.

Dbranes, categories and supersymmetry
View Description Hide DescriptionWe show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the supersymmetry preserving branes at any point in CY moduli space, completing the proposal of IIstability.

Fundamental strings in open string theory at the tachyonic vacuum
View Description Hide DescriptionWe show that the worldvolume theory on a brane at the tachyonic vacuum has solitonic string solutions whose dynamics is governed by the Nambu–Goto action of a string moving in dimensional space–time. This provides strong evidence for the conjecture that at this vacuum the full dimensional Poincaré invariance is restored. We also use this result to argue that the open string field theory at the tachyonic vacuum must contain closed string excitations.

Sigma model approach to string theory effective actions with tachyons
View Description Hide DescriptionMotivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the sigma model approach. In particular, we demonstrate that the renormalized partition function of the boundary sigma model gives the effective action for massless vectors which is consistent with the string Smatrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of in nonAbelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure but it vanishes in the NSR string case.

NonAbelian Born–Infeld and kappasymmetry
View Description Hide DescriptionWe define an iterative procedure to obtain a nonAbelian generalization of the Born–Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappasymmetry. In this paper we will present all bosonic terms in the action up to terms quartic in the Yang–Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric traceprescription.

The future of string theory
View Description Hide DescriptionProphesy is just for fun. The more useful purpose of the exercise is to identify important issues and to stimulate thought about where they stand and how they might be resolved. The subject areas that are fair game include all of particle physics and cosmology.
 ADS/CFT DUALITY

An exact prediction of supersymmetric Yang–Mills theory for string theory
View Description Hide DescriptionWe propose that the expectation value of a circular BPSWilson loop in supersymmetric Yang–Mills can be calculated exactly, to all orders in a expansion and to all orders in Using the AdS/CFT duality, this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in α^{′} and to all orders in We then compare this result with string theory. We find that the gauge theory calculation, for large and to all orders in the expansion, does agree with the leading string theory calculation, to all orders in and to lowest order in α^{′}. We also find a relation between the expectation value of any closed smooth Wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity, and compare this result, again successfully, with string theory.

Finite N AdS/CFT correspondence for Abelian and nonAbelian orbifolds, and gauge coupling unification
View Description Hide DescriptionAlthough the AdS/CFT correspondence is rigorous only for an infinite stack of D3branes, it can be fruitfully studied for finite as a source of gauge structures and choices for chiral fermions and complex scalars which solve the hierarchy problem by a conformal fixed point. We emphasize orbifolds where the resulting GFT has N=0 supersymmetry. The fact that the complex scalars are prescribed by the construction limits the possible spontaneous symmetry breaking. Both Abelian and nonAbelian Γ are illustrated by simple examples. An accurate in electroweak unification can be obtained, suggesting that this approach merits further study.

Strings in and the WZW model. I: The spectrum
View Description Hide DescriptionIn this paper we study the spectrum of bosonic string theory on We study classical solutions of the WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a noghost theorem for all the representations that are involved and discuss the scattering of the long string.

Strings in and the WZW model. II: Euclidean black hole
View Description Hide DescriptionWe consider the oneloop partition function for Euclidean BTZ black hole backgrounds or equivalently thermal backgrounds which are quotients of (Euclidean The oneloop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hepth/0001053. We see long strings and discrete states in agreement with the expectations.

Vertex operators for AdS3 with Ramond background
View Description Hide DescriptionThis review gives results on vertex operators for the Type IIB superstring in an background with Ramond–Ramond flux, which were presented at Strings 2000. Constraint equations for these vertex operators are derived, and their components are shown to satisfy the supergravity linearized equations of motion for the sixdimensional (2, 0) theory of a supergravity and tensor multiplet expanded around spacetime.

Superparticle and superstring in Ramond–Ramond background in the lightcone gauge
View Description Hide DescriptionWe discuss superparticle and superstring dynamics in supported by R–R 3form background using lightcone gauge approach. Starting with the superalgebra representing the basic symmetry of this background we find the lightcone superparticle Hamiltonian. We determine the harmonic decomposition of lightcone superfield describing fluctuations of type IIB supergravity fields expanded near background and thus the corresponding Kaluza–Klein spectrum. We fix the fermionic and bosonic lightcone gauges in the covariant Green–Schwarz superstring action and find the corresponding lightcone string Hamiltonian. We also obtain a realization of the generators of in terms of the superstring 2d fields in the lightcone gauge.

Representations of superconformal algebras in the correspondence
View Description Hide DescriptionWe perform a general analysis of representations of the superconformal algebras OSp(8/4, R) and in harmonic superspace. We present a construction of their highestweight UIR’s by multiplication of the different types of massless conformal superfields (“supersingletons”). In particular, all “short multiplets” are classified. Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravitytheory in antide Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.
 BRANEWORLDS

A supersymmetric type IIB Randall–Sundrum realization
View Description Hide DescriptionWe show that an earlier domain wall solution of type IIB supergravity provides a supersymmetric realization of the Randall–Sundrum braneworld, and give its tendimensional interpretation in terms of IIB 3branes. We also explain how previous nogo theorems are circumvented. In particular, whereas supergravity scalars have energy and are unable to support a positive tension brane, our scalar has and is the breathing mode of the compactification. Another essential element of the construction is the implementation of a symmetry by patching together compactifications with opposite signs for their 5form field strengths. This is thus a IIB analog of a previous 3brane realization of the Hořava–Witten orbifold. A modelocking phenomenon avoids the appearance of negative energy zeromodes in spite of the necessity of a negative tension branesource.

Braneworld Kaluza–Klein reductions and branes on the brane
View Description Hide DescriptionWe present a systematic study of a new type of consistent “braneworld Kaluza–Klein reduction,” which describes fully nonlinear deformations of codimension one objects that arise as solutions of a large class of gauged supergravitytheories in diverse dimensions, and whose worldvolume theories are described by ungauged supergravities withone half of the original supersymmetry. In addition, we provide oxidations of these ansätz which are in general related to sphere compactified higher dimensional string theory or Mtheory. Within each class we also provide explicit solutions of brane configurations localized on the worldbrane. We show that at the Cauchy horizon (in the transverse dimension of the consistently Kaluza–Klein reduced worldbrane) there is a curvature singularity for any configuration with a nonnull Riemann curvature or a nonvanishing Ricci scalar that lives in the worldbrane. Since the massive Kaluza–Klein modes can be consistently decoupled, they cannot participate in regulating these singularities.

Excision of singularities by stringy domain walls
View Description Hide DescriptionWe study supersymmetric domain walls on orbifolds. The supergravity solutions in the bulk are given by the attractor equation associated with Calabi–Yau (CY) spaces and have a naked space–time singularity at some We are looking for possibilities to cut off this singularity with the second wall by a stringy mechanism. We use the collapse of the CY cycle at which happens before and at a finite distance from the space–time singularity. In our example with three Kähler moduli the second wall is at the end of the moduli space at where also the enhancement of SU(2) gauge symmetry takes place so that The physics of the excision of a naked singularity via the enhançon in the context of domain wall has an interpretation on the heterotic side related to duality. The position of the enhançon is given by the equation

Effective theories and black hole production in warped compactifications
View Description Hide DescriptionWe investigate aspects of the fourdimensional (4D) effective description of brane world scenarios based on warped compactification on antide Sitter space. The lowenergy dynamics is described by visible matter gravitationally coupled to a “dark” conformal field theory. We give the linearized description of the 4D stress tensor corresponding to an arbitrary 5D matter distribution. In particular a 5D falling particle corresponds to a 4D expanding shell, giving a 4D interpretation of a trajectory that misses a black hole only by moving in the fifth dimension. Breakdown of the effective description occurs when either fivedimensional physics or strong gravity becomes important. In scenarios with a TeV brane, the latter can happen through the production of black holes near the TeV scale. This could provide an interesting experimental window on quantum black hole dynamics.