A world-line framework for 1<i>D</i> topological conformal <i>σ</i>-models

Baulieu, Laurent; Holanda, N. L.; Toppan, Francesco

doi:10.1063/1.4935851

Cited by 3 publications

(3 citation statements)

References 41 publications

(137 reference statements)

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“…The superalgebra ii) is the simplest example of superalgebra associated with the one-dimensional Supersymmetric Quantum Mechanics [24], where H is a Hamiltonian and Q is its (unique) square root supersymmetry operator. The superalgebra iii) enters the topological mechanics, with H playing the role of a scaling operator, see [26].…”

Section: The Minimal Z 2 -Graded Lie Superalgebrasmentioning

confidence: 99%

Classification of minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie (super)algebras and some applications

Kuznetsova,

Toppan

2021

Preprint

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This paper presents the classification, over the fields of real and complex numbers, of the minimal Z 2 × Z 2 -graded Lie algebras and Lie superalgebras spanned by 4 generators and with no empty graded sector. The inequivalent graded Lie (super)algebras are obtained by solving the constraints imposed by the respective graded Jacobi identities.A motivation for this mathematical result is to sistematically investigate the properties of dynamical systems invariant under graded (super)algebras. Recent works only paid attention to the special case of the one-dimensional Z 2 × Z 2 -graded Poincaré superalgebra.As applications, we are able to extend certain constructions originally introduced for this special superalgebra to other listed Z 2 × Z 2 -graded (super)algebras. We mention, in particular, the notion of Z 2 × Z 2 -graded superspace and of invariant dynamical systems (both classical worldline sigma models and a quantum Hamiltonian).As a further byproduct we point out that, contrary to Z 2 × Z 2 -graded superalgebras, a theory invariant under a Z 2 × Z 2 -graded algebra implies the presence of ordinary bosons and three different types of exotic bosons, with exotic bosons of different types anticommuting among themselves.

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Section: The Minimal Z 2 -Graded Lie Superalgebrasmentioning

confidence: 99%

Classification of minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie (super)algebras and some applications

Kuznetsova,

Toppan

2021

Preprint

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“…In the presence of the oscillatorial term the action is also SL(2)-invariant, but the SL(2) field transformations are trigonometric and carry the dependence on the dimensional parameter (see [9,10] for details). The superconformal topological model [1] can be regarded as a topological twisted supersymmetric version, see [11], of the N = 2 superconformal mechanics introduced in [12].…”

Section: The Bosonic Part Of the Actionmentioning

confidence: 99%

“…Its N = 2 superconformal symmetry closes an sl(2|1) superalgebra, whose generators are the sl(2) subalgebra generators H, D, K, the supersymmetry operators Q 1 , Q 2 , its conformal superpartners Q 1 , Q 2 and a u(1) R-symmetry generator (see [11] for details).…”

Section: The Bosonic Part Of the Actionmentioning

confidence: 99%

An angular dependent supersymmetric quantum mechanics with a Z2-invariant potential

Baulieu

Toppan²

2019

Nuclear Physics B

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We generalize the conformally invariant topological quantum mechanics of a particle propagating on a punctured plane by introducing a potential that breaks both the rotational and the conformal invariance down to a Z 2 angular-dependent discrete symmetry. We derive a topological quantum mechanics whose localization gauge functions give interesting self-dual equations. The model contains an order parameter and exhibits a critical phenomenon with the existence of two ground states above a critical scale. Unlike the ordinary O(2)-invariant Higgs potential, an angular-dependence is found and saddle points, instead of local maxima, appear, posing subtle questions about the existence of instantons. The supersymmetric quantum mechanical model is constructed in both the path integral and the operatorial frameworks.

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Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications

Kuznetsova

Toppan²

2021

Journal of Mathematical Physics

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This paper presents the classification over the fields of real and complex numbers, of the minimal Z2×Z2-graded Lie algebras and Lie superalgebras spanned by four generators and with no empty graded sector. The inequivalent graded Lie (super)algebras are obtained by solving the constraints imposed by the respective graded Jacobi identities. A motivation for this mathematical result is to systematically investigate the properties of dynamical systems invariant under graded (super)algebras. Recent works only paid attention to the special case of the one-dimensional Z2×Z2-graded Poincaré superalgebra. As applications, we are able to extend certain constructions originally introduced for this special superalgebra to other listed Z2×Z2-graded (super)algebras. We mention, in particular, the notion of Z2×Z2-graded superspace and of invariant dynamical systems (both classical worldline sigma models and quantum Hamiltonians). As a further by-product, we point out that, contrary to Z2×Z2-graded superalgebras, a theory invariant under a Z2×Z2-graded algebra implies the presence of ordinary bosons and three different types of exotic bosons, with exotic bosons of different types anticommuting among themselves.

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A world-line framework for 1D topological conformal σ-models

Cited by 3 publications

References 41 publications

Classification of minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie (super)algebras and some applications

Classification of minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie (super)algebras and some applications

An angular dependent supersymmetric quantum mechanics with a Z2-invariant potential

Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications

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