Higher Spin Lifshitz Theories and the KdV-Hierarchy

Abstract

In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.

40 pages, no figures

References in corpus (5)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Elements of Vasiliev theory
• Lifshitz Holography with Isotropic Scale Invariance
• Higher Spin Lifshitz Theory and Integrable Systems

Cited by in corpus (8)

• Lifshitz holography
• Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
• Phase space holography with no strings attached
• Constraining all possible Korteweg-de Vries type hierarchies
• Higher Spin Chern-Simons Theory and the Super Boussinesq hierarchy
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity