W-Infinity and String Theory

Abstract

We review some recent developments in the theory of $W_{\infty }$. We comment on its relevance to lower-dimensional string theory.

46 pages

References in corpus (3)

• Classical and Quantum W-Gravity
• $SL(\infty ,R)$ Symmetry of $W_{\infty }$ Gravity
• Remarks on the Physical States and the Chiral Algebra of 2D Gravity Coupled to $C\le 1$ Matter

Cited by in corpus (38)

• W-symmetry in Conformal Field Theory
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Celestial chiral algebras, colour-kinematics duality and integrability
• Large N Limit in the Quantum Hall Effect
• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase
• Algebraic Quantization, Good Operators and Fractional Quantum Numbers
• Algebraic Aspects of the Fractional Quantum Hall Effect
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• String Theory, Black Holes, and SL(2,R) Current Algebra
• Discrete State Moduli of String Theory from c=1 Matrix Model
• Unitarity in three-dimensional flat space higher spin theories
• W-Infinity Algebras from Noncommutative Chern-Simons Theory
• W-algebras from symplectomorphisms
• Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity
• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
• Higher-U(2,2)-spin fields and higher-dimensional W-gravities: quantum AdS space and radiation phenomena
• String Beta Function Equations From c=1 Matrix Model
• Linear canonical transformations and quantum phase:a unified canonical and algebraic approach
• Generalized W(infinity) Higher-Spin Algebras and Symbolic Calculus on Flag Manifolds
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• The geometry of W3 algebra: a twofold way for the rebirth of a symmetry
• Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces
• Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models
• Conformal Fluid Dynamics
• The role of complex structures in w-symmetry
• Categorical Foundation of Quantum Mechanics and String Theory
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• Moyal product and Generalized Hom-Lie-Virasoro symmetries in Bloch electron systems
• W-(infinity)-algebras in n complex dimensions and Kodaira-Spencer deformations : a symplectic approach
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Quantum dynamics of the effective field theory of the Calogero-Sutherland model
• W-hairs of black holes in three dimensional spacetime
• Perturbatively Exact $w_{1+\infty }$ Asymptotic Symmetry of Quantum Self-Dual Gravity
• A new class of Matrix Models arising from the W-infinity Algebra
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations