On a  ℤ2n-Graded Version of Supersymmetry

Bruce, Andrew James

doi:10.3390/sym11010116

Cited by 50 publications

(62 citation statements)

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“…The present work is motivated by the recently introduced Z 2 × Z 2 -graded analogue of supersymmetric and superconformal quantum mechanics [8][9][10][11]. It consists of models of one particle quantum mechanics on a real line whose symmetries are described by Z 2 × Z 2 -graded Lie superalgebras.…”

Section: Introductionmentioning

confidence: 99%

“…For a better understanding of the results in [8][9][10][11], one may pose the following question: is it possible to recover and extend these given models by quantizing some classical system? This question relies on a more essential one, namely, are there examples of classical systems invariant under the Z 2 ×Z 2 -graded supersymmetric transformations?…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

Aizawa

Kuznetsova

Toppan³

2020

Eur. Phys. J. C

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$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$Z2×Z2-graded mechanics admits four types of particles: ordinary bosons, two classes of fermions (fermions belonging to different classes commute among each other) and exotic bosons. In this paper we construct the basic $${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$Z2×Z2-graded worldline multiplets (extending the cases of one-dimensional supersymmetry) and compute, based on a general scheme, their invariant classical actions and worldline sigma-models. The four basic multiplets contain two bosons and two fermions. They are (2, 2, 0), with two propagating bosons and two propagating fermions, $$(1,2,1)_{[00]}$$(1,2,1)[00] (the ordinary boson is propagating, while the exotic boson is an auxiliary field), $$(1,2,1)_{[11]}$$(1,2,1)[11] (the converse case, the exotic boson is propagating, while the ordinary boson is an auxiliary field) and, finally, (0, 2, 2) with two bosonic auxiliary fields. Classical actions invariant under the $${{\mathbb {Z}}}_2\times {\mathbb {Z}}_2$$Z2×Z2-graded superalgebra are constructed for both single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess a full $${{\mathbb {Z}}}_2\times {\mathbb {Z}}_2$$Z2×Z2-graded conformal invariance spanned by 10 generators and containing an sl(2) subalgebra.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

Aizawa

Kuznetsova

Toppan³

2020

Eur. Phys. J. C

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“…For instance, using equations (14), it is possible to write down Serre relations [30] satisfied by the Chevalley generatorsẼ i,i+1 andẼ i+1,i of gl(m 1 , m 2 |n 1 , n 2 ). In some cases, the relative signs of the coefficients in the relations may change as a result of equations (12) and (13), which is particularly evident in the cases where one of the labels m 1 , m 2 , n 1 or n 2 is zero. Such a presentation would allow, for example, one to develop the quantum analogue and express the relations of the associated quantum group along the lines of [31][32][33].…”

Section: Discussionmentioning

confidence: 99%

The Z2×Z2-graded general linear Lie superalgebra

Isaac

Stoilova

Jeugt

2020

Journal of Mathematical Physics

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We present a novel realisation of the Z 2 ×Z 2 -graded Lie superalgebra gl(m 1 , m 2 |n 1 , n 2 ) inside an algebraic extension of the enveloping algebra of the Z 2 -graded Lie superalgebra gl(m|n), with m = m 1 + m 2 and n = n 1 + n 2 . A consequence of this realisation is that the representations of gl(m|n) "lift up" to representations of gl(m 1 , m 2 |n 1 , n 2 ), with matrix elements differing only by a sign, which we are able to characterise concisely.

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“…in the sign convention we have adopted (see [11] for the analogous formulas in the opposite convention and [12,13] for further recent work in our convention). Using these operators, N number operatorsp A can be defined asp 6) where no summation in A is implied.…”

Section: Defining the Calculusmentioning

confidence: 99%

Graded Geometry and Tensor Gauge Theories

Chatzistavrakidis¹,

Karagiannis²,

Schupp³

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that a given Lagrangian describes the dynamics of any type of bosonic tensor field even though the corresponding explicit expressions in terms of local field components and their derivatives look rather different. Aside from free fields and their kinetic terms, we also consider higher derivative interaction terms that lead to second order field equations. For scalars, differential forms and bipartite tensors, these are identified with Galileon theories, written in a simple yet elegant form as a generalised kinetic term, and are gauge invariant by construction. For fields of spin higher than 2, we illustrate the candidate Galileon-like interactions and argue that full gauge invariance and locality cannot be simultaneously maintained.

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On a ℤ2n-Graded Version of Supersymmetry

Cited by 50 publications

References 72 publications

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

The Z2×Z2-graded general linear Lie superalgebra

Graded Geometry and Tensor Gauge Theories

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