Higher spin Chern–Simons theory and the super Boussinesq hierarchy

Gutperle, Michael; Li, Yang

doi:10.1142/s0217751x18500859

Cited by 2 publications

(2 citation statements)

References 30 publications

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“…Further interesting links between certain well-known classes of integrable systems and higher spin gravity on AdS 3 have been explored in [104], [105], [106], [68], [107]. read H (0)…”

Section: Extensions Of Our Resultsmentioning

confidence: 99%

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

Fuentealba

Matulich

Pérez

et al. 2018

J. High Energ. Phys.

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We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS 3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions.The analysis is performed in terms of two-dimensional gauge fields for isl(2, R), being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS 3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k.Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.

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“…Further interesting links between certain well-known classes of integrable systems and higher spin gravity on AdS 3 have been explored in [104], [105], [106], [68], [107]. read H (0)…”

Section: Extensions Of Our Resultsmentioning

confidence: 99%

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

Fuentealba

Matulich

Pérez

et al. 2018

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…These are not the only interesting features that have been explored in the context of Lifschitz holography using higher spin symmetries. Also very interesting relations to integrable systems have been discovered in [88][89][90]…”

Section: Lifschitz Spacetimesmentioning

confidence: 97%

Higher Spins without (Anti-)de Sitter

Prohazka

Riegler

2018

Universe

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Can the holographic principle be extended beyond the well-known AdS/CFT correspondence? During the last couple of years, there has been a substantial amount of research trying to find answers for this question. In this work, we provide a review of recent developments of three-dimensional theories of gravity with higher spin symmetries. We focus in particular on a proposed holographic duality involving asymptotically flat spacetimes and higher spin extended bms 3 symmetries. In addition, we also discuss developments concerning relativistic and nonrelativistic higher spin algebras. As a special case, Carroll gravity will be discussed in detail.

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Higher spin Chern–Simons theory and the super Boussinesq hierarchy

Cited by 2 publications

References 30 publications

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

Higher Spins without (Anti-)de Sitter

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