$W_{1+\infty }$ constraints for the hermitian one-matrix model

Abstract

We construct the multi-variable realizations of the $W_{1+\infty }$ algebra such that they lead to the $W_{1+\infty }$ $n$-algebra. Based on our realizations of the $W_{1+\infty }$ algebra, we derive the $W_{1+\infty }$ constraints for the hermitian one-matrix model. The constraint operators yield not only the $W_{1+\infty }$ algebra but also the closed $W_{1+\infty }$ $n$-algebra.

arXiv comment14 pages

References in corpus (16)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Infinite Symmetry in the Quantum Hall Effect
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• n-ary algebras: a review with applications
• Ding-Iohara-Miki symmetry of network matrix models
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• Noncommutative geometry for three-dimensional topological insulators
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• D-Algebra Structure of Topological Insulators
• Multi-operator brackets acting thrice
• Ternutator Identities
• Higher spins from Nambu-Chern-Simons theory

Cited by in corpus (3)

• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Correlators in the supereigenvalue model in the Ramond sector
• Exact correlators in the Gaussian Hermitian matrix model