The heterotic string is a soliton

It is shown that the Type IIA superstring compactified on K3 has a smooth string soliton with the same zero mode structure as the heterotic string compactified on a four-torus, thus providing new evidence for a conjectured exact duality between the two six-dimensional string theories. The chiral worldsheet bosons arise as zero modes of Ramond-Ramond fields of the IIA string theory and live on a signature (20,4) even, self-dual lattice. Stable, finite loops of soliton string provide the charged Ramond-Ramond states necessary for enhanced gauge symmetries at degeneration points of the K3 surface. It is also shown that Type IIB strings toroidally compactified to six dimensions have a multiplet of string solutions with Type II worldsheets.     

Rotational invariance in the M(atrix) formulation of type IIB theory

The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.     

Strings as solitons & black holes as strings

Supersymmetric closed string theories contain an infinite tower of BPS-saturated, oscillating, macroscopic strings in the perturbative spectrum. When these theories have dual formulations, this tower of states must exist nonperturbatively as solitons in the dual theories. We present a general class of exact solutions of low-energy supergravity that corresponds to all these states. After dimensional reduction they can be interpreted as supersymmetric black holes with a degeneracy related to the degeneracy of the string states. For example, in four dimensions we obtain a point-like solution which is asymptotic to a stationary, rotating, electrically-charged black hole with Regge-bounded angular momentum and with the usual ring-singularity replaced by a string source. This further supports the idea that the entropy of supersymmetric black holes can be understood in terms of counting of string states. We also discuss some applications of these solutions to string duality.     

Extending Dualities to Trialities Deepens the Foundations of Dynamics

Dualities are often supposed to be foundational, but they may come into conflict with a strong form of background independence, which is the principle that the dynamical equations of a theory not depend on arbitrary, fixed, non-dynamical structures. This is because a hidden fixed structures is needed to define the duality transformation. Examples include a fixed, absolute notion of time, a fixed non-dynamical background geometry, or the metric of Hilbert space. We show that this conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, which have a natural triality symmetry. We show how breaking this triality symmetry by imposing different compactifications, which are expansions around fixed classical solutions, yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born’s duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.     

String cosmology

In this review, we discuss various cosmological issues related to our Universe from a string theoretic perspective. We analyse the pre-big bang cosmological scenario which appears naturally in this context due to the existence of scale factor duality symmetry in string theory. We then discuss some of the attractive and problematic features of this scenario. Finally, we introduce a method which is powerful enough to search for cosmological solutions in various low energy limits of string theories.     

Hadron potentials within the gauge/string correspondence

It is known, since the 70s, that the large N 't Hooft limit of gauge theories is related to string theories. In 1998, J. M. Maldacena identified precisely such a relation: the so-called AdS/CFT correspondence which speculates a duality between a large N strongly-coupled supersymmetric and conformal Yang-Mills theory in four dimensions and a weakly-coupled string theory defined in a five-dimensional anti-de Sitter AdS₅ space-time. This review aims at introducing concepts and methods used to derive, in the framework of the gauge/string correspondence, the interaction potentials of mesons and baryons at zero and finite temperature. The dual string configurations associated with the different kinds of hadrons are described and their behaviours at short and large distances are understood. Although the application of Maldacena's AdS/CFT conjecture to QCD is not straightforward, QCD being neither supersymmetric nor conformal, the AdS/QCD correspondence approach attempts to identify the dual theory of QCD. Especially, the study of heavy quark-antiquark bound-states leads to establish general dual criteria for the confinement.     

Unraveling AdS/CFT

In this review, I survey the conjectured correspondence between a string theory in ten dimensions and certain supersymmetric gauge theories in four. This duality has recently garnered considerable attention from scientists studying the hot matter produced in heavy-ion collisions. An important and immediate question is to what extent one can hope to describe the dynamics of the quark–gluon plasma in a supersymmetric conformal field theory. Here I explain recent applications of the AdS/CFT correspondence to the strongly interacting matter produced at the Relativistic Heavy Ion Collider. Progress in characterizing the medium with these techniques will be discussed, as well as limitations inherent to the method.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

New principles for string/membrane unification

The target space theory of the N = (2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either 1 + 1 or 2 + 1 dimensions. Among the target space theories in 1 + 1 dimensions are the bosonic, type II, and heterotic string world-sheet field theories in a physical gauge. The (2 + 1)-dimensional version describes a consistent quantum theory of supermembranes in 10 + 1 dimensions. The unifying framework for all of these vacua is a theory of (2 + 2)-dimensional self-dual geometries embedded in 10 + 2 dimensions. There are also indications that the N = (2,1) string describes the strong-coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.     

M-theory: Strings,duality and branes

String theory is an attempt to combine all of the known physical forces into a single unified framework. A powerful new type of duality symmetry has recently been discovered in string theory which has led to important breakthroughs. What were previously considered to be five distinct string theories are now known to be different aspects of an underlying structure called M-theory. In addition to strings, extended objects of higher dimension or 'branes', play a key role. We review these developments and discuss the impact that they are having on quantum field theory and the quantum properties of black holes.     

Operators with Large R-Charge in N=4 Yang-Mills Theory

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong-weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well-defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two-loop level that the anomalous dimension has a finite limit when the R-charge J→∞ keeps λ/J² finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.     

Construction of instanton and monopole solutions and reciprocity

An elementary argument demonstrating the completeness of the Atiyah-Drinfeld-Hitchin-Manin construction of self-dual instanton solutions to Euclidean gauge theories is presented. The adaptation of this discussion to Nahm's construction for SU(2) monopoles is outlined. These constructions are shown to establish a reciprocity or duality between self-dual theories in zero and four dimensions and in one and three dimensions, respectively.     

Non-supersymmetric gauge theories from D-branes in type 0 string theory

We construct non-supersymmetric four-dimensional gauge theories arising as effective theories of D-branes placed on various singularities in Type 0B string theory. We mostly focus on models which are conformal in the large-N limit and present both examples appearing on self-dual D3-branes on orbifold singularities and examples including orientifold planes. Moreover, we derive type 0 Hanany-Witten setups with NS 5-branes intersected by D-branes and the corresponding rules for determining the massless spectra. Finally, we discuss possible duality symmetries (Seiberg duality) for non-supersymmetric gauge theories within this framework.     

A class of 6D conformal field theories: relation to 4D superconformal Yang-Mills theories?

We describe a class of six-dimensional conformal field theories that possibly are related to the tensionless string theories. They have an ADE classification, but no other discrete or continuous parameters, with the A(N-1) theory arising by factoring out the collective "center of mass" degrees of freedom from N noninteracting chiral two-forms. The Hilbert space carries an irreducible representation of the same Heisenberg group that appears in the tensionless string theories, and the "Wilson surface" observables obey the same superselection rules. When compactified on a two-torus, our theories have the same behavior under S duality as N = 4 super Yang-Mills theories.     

String tensions for lattice gauge theories in 2 + 1 dimensions

Compact U(1) and SU(2) lattice gauge theories in 3 euclidean dimensions are studied by standard Monte Carlo techniques. The question of extracting reliable string tensions from these theories is examined in detail, including a comparison of the Monte Carlo Wilson loop data with weak coupling predictions and a careful error analysis: our conclusions are rather different from those of previous investigations of these theories. In the case of U(1) theory, we find that only a tiny range of β values can possibly be relevant for extracting a string tension and we are unable to convincingly demonstrate the expected exponential dependence of the string tension on β. For the SU(2) theory we are able to determine, albeit with rather large errors, a string tension from a study of Wilson loops.     

String Geometry and the Noncommutative Torus

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra ? and the noncommutative torus. We show that the tachyon algebra of ? is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;ℤ) Morita equivalences between d-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang–Mills gauge theory minimally coupled to massive Dirac fermion fields. Received: 26 October 1998/ Accepted: 9 April 1999     

Nonlocal instantons and solitons in string models

We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski, Friedmann–Robertson–Walker and Euclidean metric backgrounds. Starting from distribution-like initial field configurations which are constant almost everywhere, we construct exact and approximate nonlocal solutions. The Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean kink of supersymmetric open string field theory as an instanton. Some relations between solutions of different string theories are highlighted also thanks to a reformulation of nonlocal systems as fixed points in a renormalization group flow.     

Supersymmetrical string theories

A supersymmetrical light-cone-gauge string action is presented. It provides a basis for understanding the previously- studied supersymmetrical dual string theory as well as two new closed-string theories that have extended supersymmetry in ten dimensions, corresponding to N=8 supersymmetry in four dimensions.     

Lower dimensional black holes

A survey of black hole physics in two spacetime dimensions is presented. Basic properties, specific solutions and quantum aspects are considered in turn. The relationship between string theoretic black holes and those arising in other (1+l)-dimensional theories of gravity is discussed.