Quantum string integrability and AdS/CFT

Recent explorations of the AdS/CFT correspondence have unveiled integrable structures underlying both planar N = 4 super-Yang-Mills theory and type IIB string theory on AdS_5 x S^5. Integrability in the gauge theory emerges from the fact that the dilatation generator can be identified with the Hamiltonian of an integrable quantum spin chain, and the classical string theory has been shown to contain infinite towers of hidden currents, a typical signature of integrability. Efforts to match the integrable structures of various classical string configurations to those of corresponding gauge theory quantum spin chains have been largely successful. By studying a semiclassical expansion about a class of point-like solitonic solutions to the classical string equations of motion on AdS_5 x S^5, we take a step toward demonstrating that integrability in the string theory survives quantum corrections beyond tree level. Quantum fluctuations are chosen to align with background curvature corrections to the pp-wave limit of AdS_5 x S^5, and we present evidence for an infinite tower of local bosonic charges that are conserved by the quantum theory to quartic order in the expansion. We explicitly compute several higher charges based on a Lax representation of the worldsheet sigma model and provide a prescription for matching the eigenvalue spectra of these charges with corresponding quantities descending from the integrable structure of the gauge theory.Comment: v2: references and typos corrected; v3: minor corrections and comments, 23 page

Charting the landscape of supercritical string theory

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions (via dimension quenching) and different amounts of worldsheet supersymmetry (via c-duality). These solutions connect supercritical string theories to the more familiar string duality web in ten dimensions, and provide a precise link between supersymmetric and purely bosonic string theories. Dimension quenching and c-duality appear to be natural concepts in string theory, giving rise to large networks of interconnected theories. We describe some of these networks in detail and discuss general consistency constraints on the types of transitions that arise in this framework.Comment: 27 pages, 4 figure

Boundary Operators in Effective String Theory

Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are relevant for the controlled study of open relativistic strings with freely moving endpoints. Relativistic open strings are thought to encode the dynamics of confined quark-antiquark pairs in gauge theories in the planar approximation. Neumann boundary operators can be organized by their behavior under scaling of the target space coordinates X, and the set of allowed X-scaling exponents is bounded above by +1/2 and unbounded below. Negative contributions to X-scalings come from powers of a single invariant, or "dressing" operator, which is bilinear in the embedding coordinates. In particular, we show that all Neumann boundary operators are dressed by quarter-integer powers of this invariant, and we demonstrate how this rule arises from various ways of regulating the short-distance singularities of the effective theory.Comment: LaTeX, 37 page

Cosmological solutions of supercritical string theory

We study quintessence-driven, spatially flat, expanding FRW cosmologies that arise naturally from string theory formulated in a supercritical number of spacetime dimensions. The tree-level potential of the string theory produces an equation of state at the threshold between accelerating and decelerating cosmologies, and the resulting spacetime is globally conformally equivalent to Minkowski space. We demonstrate that exact solutions exist with a condensate of the closed-string tachyon, the simplest of which is a Liouville wall moving at the speed of light. We rely on the existence of this solution to derive constraints on the couplings of the tachyon to the dilaton and metric in the string theory effective action. In particular, we show that the tachyon dependence of the Einstein term must be nontrivial.Comment: v2: typos corrected and references added; v3: minor corrections; 35 pages, 9 figure

Cosmology of the closed string tachyon

The spacetime physics of bulk closed string tachyon condensation is studied at the level of a two-derivative effective action. We derive the unique perturbative tachyon potential consistent with a full class of linearized tachyonic deformations of supercritical string theory. The solutions of interest deform a general linear dilaton background by the insertion of purely exponential tachyon vertex operators. In spacetime, the evolution of the tachyon drives an accelerated contraction of the universe and, absent higher-order corrections, the theory collapses to a cosmological singularity in finite time, at arbitrarily weak string coupling. When the tachyon exhibits a null symmetry, the worldsheet dynamics are known to be exact and well-defined at tree level. We prove that if the two-derivative effective action is free of non-gravitational singularities, higher-order corrections always resolve the spacetime curvature singularity of the null tachyon. The resulting theory provides an explicit mechanism by which tachyon condensation can generate or terminate the flow of cosmological time in string theory. Additional particular solutions can resolve an initial singularity with a tachyonic phase at weak coupling, or yield solitonic configurations that localize the universe along spatial directions.Comment: 48 pages, 14 figures; v2: references adde