A classification of lowest weight irreducible modules over $\mathbb{Z}_2^2$-graded extension of $osp(1|2)$

Amakawa, K.; Aizawa, N.

doi:10.48550/arxiv.2011.03714

Cited by 2 publications

(4 citation statements)

References 55 publications

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“…The physical interpretation of x as en extra dimension induced by the exotic bosonic coordinate will be discussed in the following. The component fields entering (30) are defined in p1 `1q-dimensions; the graded superfield can be associated with the symbol below which specifies the numbers of component fields, see formula (26), of respective scaling dimension s, s `1 2 , s `1, s `3 2 , s `2: p1; 2; 2; 2; 1q. (34) Analogous symbols have been employed to describe representations of one-dimensional supermechanics [36,37] and of one-dimensional Z 2 ˆZ2 -graded mechanics [13].…”

Section: The Graded Superspacementioning

confidence: 99%

“…On the mathematical side various studies of algebraic and geometric aspects of Z n 2 -graded structures have been investigated since their introduction. Here we mention only very recent works of algebraic studies which discuss structures and representations [26][27][28][29] (further references on algebraic aspects are found in [26]). The differential geometry on Z n 2 -graded manifolds, which has a close kinship with the Z 2 ˆZ2 -graded superspace formulation, is also a field of extensive study; for details one can see the concise reviews [30,31].…”

Section: Introductionmentioning

confidence: 99%

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New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

Aizawa¹,

Ren²,

Kuznetsova³

et al. 2023

Preprint

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A novel feature of the Z 2 ˆZ2 -graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the "exotic bosonic coordinate" was not considered by previous works on the one-dimensional Z 2 ˆZ2 -graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained. The graded superspace calculus of the Z 2 ˆZ2 -graded worldline super-Poincaré algebra induces two-dimensional Z 2 ˆZ2 -graded relativistic models; they are invariant under a new Z 2 ˆZ2 -graded 2D super-Poincaré algebra which differs from the previous two Z 2 ˆZ2graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S 1 , a Z 2 ˆZ2 -graded closed string with periodic boundary conditions is derived. The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger pβ-deformed, where β ě 0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β " 0) is obtained. While the spectrum of the β " 0 point-particle models is degenerate (due to its relation with an N " 2 supersymmetry), this is no longer the case for the β ą 0 models.

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Section: The Graded Superspacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

Aizawa¹,

Ren²,

Kuznetsova³

et al. 2023

Preprint

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“…It is shown that by this realization many models of the standard SCQM are mapped to their Z 2 2 -graded extension. The simplest case, Z 2 2 -graded osp(1|2) SCQM, is investigated in some detail [3] and abstract representation theory of Z 2 2 -graded osp(1|2) is developed in [11] where the richness of irreducible representations of Z 2 2 -graded osp(1|2) is observed. As a continuation of the works on quantum mechanical realizations of Z n 2 -graded Lie superalgebras, in the present work we explore Z n 2 -graded version of SCQM and present models of Z 3 2 -graded SCQM explicitly.…”

Section: Introductionmentioning

confidence: 99%

“…In mathematics side, Z n 2 -graded supergeometry which is an extension of supergeometry on supermanifolds, is studied extensively, see e.g., [19]. More exhaustive list of references of physical and mathematical aspects of Z n 2 -graded Lie superalgebras is found in [11].…”

Section: Introductionmentioning

confidence: 99%

$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

Doi,

Aizawa

2021

Preprint

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Quantum mechanical systems whose symmetry is given by Z 3 2 -graded version of superconformal algebra are introduced. This is done by finding a realization of a Z 3 2 -graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models of superconformal quantum mechanics (SCQM) to their Z 3 2 -graded extensions. It is observed that for the simplest SCQM with osp(1|2) symmetry there exist two inequivalent Z 3 2 -graded extensions. Applying the standard prescription of conformal quantum mechanics, spectrum of the SCQMs with the Z 3 2 -graded osp(1|2) symmetry is analyzed. It is shown that many models of SCQM can be extended to Z n 2 -graded setting.

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A classification of lowest weight irreducible modules over $\mathbb{Z}_2^2$-graded extension of $osp(1|2)$

Cited by 2 publications

References 55 publications

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

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