Super-GCA from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>super-Virasoro

Mandal, Ipsita; Rayyan, Ahmed

doi:10.1016/j.physletb.2016.01.031

Cited by 15 publications

(16 citation statements)

References 47 publications

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“…Another aspect that it would be worth exploring is the connection of our new infinite-dimensional superalgebras with the two-dimensional super Galilean conformal algebra (GCA) [70,71,103]. In particular, one could expect to obtain a deformed super-GCA algebra by contracting the relativistic (1, 1) Superconformal ⊕ Virasoro algebra obtained here.…”

Section: Discussionmentioning

confidence: 96%

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

et al. 2020

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In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-BM S 3 , the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the so(2, 2) ⊕ so(2, 1) gravity theories. We extend our results to the N = 2 and N = 4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit ℓ → ∞. Conclusions 316 Acknowledgment 32

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Section: Discussionmentioning

confidence: 96%

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

et al. 2020

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“…Representation theories and supersymmetric extensions of ℓ-GCA for higher values of d have not been studied extensively. As found in the literatures [45,48,49,50,51,52,53], supersymmetric extension of g ℓ is not unique and some of them are discussed in connection with tensionless string theory. This implies that starting from bosonic ℓ-GCA for higher values of d one may obtain various infinite dimensional superalgebras and some of them are of physical interest.…”

Section: Discussionmentioning

confidence: 96%

“…Supersymmetric extensions found in literatures are also restricted to ℓ = 1 algebra. Such extensions are considered again in the context of infinite dimensional GCA [45,46,61], BMS group [47,48,49], generalized Sturm-Liouville operators [50,51] and string theory [52,53]. We introduce a supersymmetric extension of the algebra (1.2) for any values of ℓ, and classify its central extensions.…”

Section: Introductionmentioning

confidence: 99%

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Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Aizawa

Segar

2016

Journal of Mathematical Physics

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In this work we construct a infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.

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“…The BMS 3 algebra also naturally arises in diverse contexts of physical interest. For instance, it describes the worldsheet symmetries of the bosonic sector in the tensionless limit of closed string theory [8], [9], [10], [11], [12], [13], [14], [15], and it is then expected to be relevant for the description of interacting higher spin fields [16], [17], [18], [19], [20] (for a review, see e.g. [21]).…”

Section: Introductionmentioning

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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Super-GCA fromN=(2,2)super-Virasoro

Cited by 15 publications

References 47 publications

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

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

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