Higher spin Lifshitz theory and integrable systems

Gutperle, Michael; Yi, Li

doi:10.1103/physrevd.91.046012

Cited by 15 publications

(24 citation statements)

References 64 publications

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“…It is worth pointing out that prescribing the asymptotic behaviour of gauge fields to be described by deviations with respect to a reference background that go along the highest weight generators of the algebra, turns out to be a very successful strategy. Indeed, this is not only the case of General Relativity in three spacetime dimensions [28], but it is also so for its locally supersymmetric extension with or without cosmological constant [44], [21], or even when the theory is nonminimally coupled to higher spin fields [45], [46], [47], [26], [27], [19], [48], [20], [17], [18], [49].…”

Section: Final Remarksmentioning

confidence: 99%

Asymptotically flat structure of hypergravity in three spacetime dimensions

Fuentealba

Matulich

Troncoso

2015

J. High Energ. Phys.

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The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-5/2 field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS 3 . It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W (2,4) algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined "Killing vector-spinors". The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or antiperiodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s + 1 2 in the energy, where s is the spin of the fermionic generators.

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Section: Final Remarksmentioning

confidence: 99%

Asymptotically flat structure of hypergravity in three spacetime dimensions

Fuentealba

Matulich

Troncoso

2015

J. High Energ. Phys.

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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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“…More details can be found, for example, in [12,17]. In addition, we review some the results obtained in previous papers of some of the authors on the formulation of theories with Lifshitz scaling in higher spin gravity theories [18] and the relation of these theories to the KdV hierarchy [20].…”

Section: Review Of Higher Spin Lifshitz Theoriesmentioning

confidence: 96%

“…Note that the barred connection in (2.13) can be related to the unbarred sector by a conjugation operationĀ = A c , where the conjugation is acting on the gauge algebra generator by (V s m ) c = (−1) s+m+1 V s −m . Though in general A andĀ maybe unrelated, A c solves the flatness condition in the barred sector if A solves it in the unbarred sector so we always takeĀ to be A c as in [20]. By this choice we can get the Lifshitz metric from (2.5).…”

Section: )mentioning

confidence: 99%

Higher spin Lifshitz theories and the Korteweg-de Vries hierarchy

Beccaria

Gutperle

et al. 2015

Phys. Rev. D

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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.

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Higher spin Lifshitz theory and integrable systems

Abstract: In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three-dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.

Cited by 15 publications

References 64 publications

Asymptotically flat structure of hypergravity in three spacetime dimensions

Asymptotically flat structure of hypergravity in three spacetime dimensions

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

Higher spin Lifshitz theories and the Korteweg-de Vries hierarchy

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