Ian Swanson

Quantizing string theory in AdS5×S5: beyond the pp-wave

In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge world-sheet action for a type IIB superstring on AdS5 × S 5 reduces to that of a free field theory. It has been conjectured by Berenstein, Maldacena, and Nastase that the energy spectrum of this string theory matches the dimensions of operators in the appropriately defined large R-charge large-Nc sector of N = 4 supersymmetric Yang–Mills theory in four dimensions. This holographic equivalence is thought to be exact, independent of any simplifying kinematic limits. As a step toward verifying this larger conjecture, we have computed the complete set of first curvature corrections to the spectrum of light-cone gauge string theory that arises in the expansion of AdS5 × S 5 about the plane-wave limit. The resulting spectrum has the complete dependence on λ = g 2 Y M Nc; corresponding results in the gauge theory are known only to second order in λ. We find precise agreement to this order, including the N = 4 extended supermultiplet structure. In the process, we demonstrate that the complicated schemes put forward in recent years for defining the Green–Schwarz superstring action in background Ramond-Ramond fields can be reduced to a practical (and correct) method for quantizing the string.

Holography beyond the Penrose limit

The flat pp-wave background geometry has been realized as a particular Penrose limit of AdS5 × S 5 . It describes a string that has been infinitely boosted along an equatorial null geodesic in the S 5 subspace. The string worldsheet Hamiltonian in this background is free. Finite boosts lead to curvature corrections that induce interacting perturbations of the string worldsheet Hamiltonian. We develop a systematic light-cone gauge quantization of the interacting worldsheet string theory and use it to obtain the interacting spectrum of the so-called ‘two-impurity’ states of the string. The quantization is technically rather intricate and we provide a detailed account of the methods we use to extract explicit results. We give a systematic treatment of the fermionic states and are able to show that the spectrum possesses the proper extended supermultiplet structure (a non-trivial fact since half the supersymmetry is nonlinearly realized). We test holography by comparing the string energy spectrum with the scaling dimensions of corresponding gauge theory operators. We confirm earlier results that agreement obtains in low orders of perturbation theory, but breaks down at third order. The methods presented here can be used to explore these issues in a wider context than is specifically dealt with in this paper.

Cosmological solutions of supercritical string theory

We study quintessence-driven, spatially flat, expanding Friedmann-Robertson-Walker 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.

Dimension-changing exact solutions of string theory

Superstring theories in the critical dimension D = 10 are connected to one another by a well-explored web of dualities. In this paper we use closed-string tachyon condensation to connect the supersymmetric moduli space of the critical superstring to non-supersymmetric string theories in more than ten dimensions. We present a new set of classical solutions that exhibit dynamical transitions between string theories in different dimensions, with different degrees of stability and different amounts of spacetime supersymmetry. In all examples, the string-frame metric and dilaton gradient readjust themselves during the transition. The central charge of the worldsheet theory remains equal to 15, even as the total number of dimensions changes. This phenomenon arises entirely from a one-loop diagram on the string worldsheet. Allowed supersymmetric final states include half-BPS vacua of type II and SO(32) heterotic string theory. We also find solutions that bypass the critical dimension altogether and proceed directly to spacelike linear dilaton theories in dimensions greater than or equal to two.

Integrable twists in AdS/CFT

A class of marginal deformations of four-dimensional = 4 super Yang-Mills theory has been found to correspond to a set of smooth, multiparameter deformations of the S5 target subspace in the holographic dual on AdS5 ? S5. We present here an analogous set of deformations that act on global toroidal isometries in the AdS5 subspace. Remarkably, certain sectors of the string theory remain classically integrable in this larger class of so-called ?-deformed AdS5 ? S5 backgrounds. Relying on studies of deformed (2)? models, we formulate a local (2)? Lax representation that admits a classical, thermodynamic Bethe equation (based on the Riemann-Hilbert interpretation of Bethes ansatz) encoding the spectrum in the deformed AdS5 geometry. This result is extended to a set of discretized, asymptotic Bethe equations for the twisted string theory. Near-pp-wave energy spectra within (2)? and (2)? sectors provide a useful and stringent test of such equations, demonstrating the reliability of this technology in a wider class of string backgrounds. In addition, we study a twisted Hubbard model that yields certain predictions of the dual ?-deformed gauge theory.

Quantum string integrability and AdS/CFT

Abstract 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 × 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 × 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 × 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.

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 and different amounts of world sheet supersymmetry. 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.

String Theory of the Regge Intercept

Using the Polchinski-Strominger effective string theory in the covariant gauge, we compute the mass of a rotating string in D dimensions with large angular momenta J, in one or two planes, in fixed ratio, up to and including first subleading order in the large J expansion. This constitutes a first-principles calculation of the value for the order-J(0) contribution to the mass squared of a meson on the leading Regge trajectory in planar QCD with bosonic quarks. For open strings with Neumann boundary conditions, and for closed strings in D≥5, the order-J(0) term in the mass squared is exactly calculated by the semiclassical approximation. This term in the expansion is universal and independent of the details of the theory, assuming only D-dimensional Poincaré invariance and the absence of other infinite-range excitations on the string world volume, beyond the Nambu-Goldstone bosons.

Open string integrability and AdS/CFT

We present a set of long-range Bethe ansatz equations for open quantum strings on AdS5 × S5 and demonstrate that they diagonalize bosonic su(2) and sl(2) sectors of the theory in the near-pp-wave limit. Results are compared with energy spectra obtained by direct quantization of the open string theory, and we find agreement in this limit to all orders in the ’t Hooft coupling [lambda] = g2Y MNc. We also propose long-range Bethe ans¨atze for su(2) and sl(2) sectors of the dual N = 2 defect conformal field theory. In accordance with previous investigations, we find exact agreement between string theory and gauge theory at one- and two-loop order in [lambda], but a general disagreement at higher loops. It has been conjectured that the sudden mismatch at three-loop order may be due to long-range interaction terms that are lost in the weak coupling expansion of the gauge theory dilatation operator. These terms are thought to include interactions that wrap around gauge-traced operators, or around the closed-string worldsheet. We comment on the role these interactions play in both open and closed sectors of string states and operators near the pp-wave/BMN limit of the AdS/CFT correspondence.

Effective string theory simplified

A bstractIn this note we simplify the formulation of the Poincaré-invariant effective string theory in D dimensions by adding an intrinsic metric and embedding its dynamics into the Polyakov formalism. We use this formalism to classify operators order-by-order in the inverse physical length of the string, in a fully gauge-invariant framework. We then use this classification to analyze the universality and nonuniversality of observables, up to and including the second sub-leading order in the long string expansion.