Integrability structures in string theory

Abstract

This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and loop variables naturally appearing in membrane dynamics. While reviewing each topic in more details we emphasize connections between them and speculate on possible relations to membrane integrability.

arXiv commentv2: refs added

References in corpus (129)

• String Theory and Noncommutative Geometry
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Unity of Superstring Dualities
• Review of AdS/CFT Integrability: An Overview
• Algebraic structures on parallel M2-branes
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• Modeling Multiple M2's
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• On Foundation of the Generalized Nambu Mechanics
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Brane Dynamics From the Born-Infeld Action
• Integrable Hierarchies and Dispersionless Limit
• Covariant Action for the Super-Five-Brane of M-Theory
• On integrability of the Yang-Baxter $\si$-model
• Foundations of the AdS_5 x S^5 Superstring. Part I
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• U-duality and M-Theory
• Lax Pair for Strings in Lunin-Maldacena Background
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Dualisation of Dualities, I
• Double Field Theory: A Pedagogical Review
• On classical q-deformations of integrable sigma-models
• On Lorentz Invariant Actions for Chiral P-Forms
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• The M2-M5 Brane System and a Generalized Nahm's Equation
• D=11, p=5
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
• Covariant Field Equations of the M Theory Five-Brane
• Exploring Double Field Theory
• D-branes, Monopoles and Nahm Equations
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• Lectures on Gauged Supergravity and Flux Compactifications
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Double Field Theory of Type II Strings
• Selfdual strings and loop space Nahm equations
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• The Self-Dual String Soliton
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• A New Approach to Integrable Theories in any Dimension
• Integrable Deformations of Strings on Symmetric Spaces
• A Noncommutative M-Theory Five-brane
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Nonabelian (2,0) Tensor Multiplets and 3-algebras
• SDiff(2) KP hierarchy
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• On deformed gauge theories and their string/M-theory duals
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• Poisson-Lie T-Duality in Double Field Theory
• Six-Dimensional Tensionless Strings In The Large N Limit
• Duality Invariance: From M-theory to Double Field Theory
• Poisson-Lie T-plurality
• A new family of $SU(2)$ symmetric integrable sigma models
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Lectures on the Bethe Ansatz
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• On Marginal Deformations and Non-Integrability
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Classification of 6-dimensional real Drinfeld doubles
• Dynamical Symmetries and Nambu Mechanics
• U-duality extension of Drinfel'd double
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Poisson-Lie U-duality in Exceptional Field Theory
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Weyl invariance for generalized supergravity backgrounds from the doubled formalism
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
• Quantum correction to generalized T-dualities
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Puzzles of eta-deformed AdS_5 x S^5
• Critical fields on the M5-brane and noncommutative open strings
• Labeling Schemes for Tetrahedron Equations and Dualities between Them
• On the Polarization of Unstable D0-Branes into Non-Commutative Odd Spheres
• Integrable theories and loop spaces: fundamentals, applications and new developments
• Integrable theories that are asymptotically CFT
• Deformation independent open brane metrics and generalized theta parameters
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
• Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz
• Weyl invariance of string theories in generalized supergravity backgrounds
• Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
• Non-Abelian U-duality for membrane
• Tri-vector deformations in $d=11$ supergravity
• Classical Yang-Baxter equation from beta-supergravity
• Lectures on S-matrices and Integrability
• Conformal anomaly of Wilson surface observables - a field theoretical computation
• Classification of Poisson-Lie T-dual models with two-dimensional targets
• Non-abelian tri-vector deformations in d=11 supergravity
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Non-integrability and Chaos with Unquenched Flavor
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Nambu bracket and M-theory
• Introduction to classical and quantum integrability
• Polyvector deformations in eleven-dimensional supergravity
• The M5-brane action revisited
• The 3-Lie Algebra (2,0) Tensor Multiplet and Equations of Motion on Loop Space
• Yang-Baxter Deformation as an O(d,d) Transformation
• String integrability of defect CFT and dynamical reflection matrices
• Constructing Self-Dual Strings
• Calibrations, Monopoles and Fuzzy Funnels
• Non-abelian U-duality at work
• Hunt for 3-Schur polynomials
• Yang-Baxter deformations and generalized supergravity -- A short summary
• An associative star-three-product and applications to M two/M five-brane theory
• On non-abelian U-duality of 11D backgrounds
• String integrability of the ABJM defect
• Generalized Supergravity Equations and Generalized Fradkin-Tseytlin Counterterm
• Wilson surface observables from equivariant cohomology
• Generalizing eleven-dimensional supergravity
• Generalised T-duality and Integrable Deformations
• Analytic Non-Integrability and S-Matrix Factorization
• Generalized 11D supergravity equations from tri-vector deformations
• Recent developments in non-Abelian T-duality in string theory
• Nonabelian D-branes and Noncommutative Geometry
• An Algebraic Classification of Solution Generating Techniques

Cited by in corpus (2)

• Polyvector deformations of Type IIB backgrounds
• Yang-Baxter structure of the extended space