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Cunha, Ivan E.; Holanda, N. L.; Toppan, Francesco

doi:10.1103/physrevd.96.065014

Cited by 17 publications

(12 citation statements)

References 58 publications

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“…This vacuum energy for the spinless system (i.e. for q = 0) coincides with the one given in [24] (for α = −1/2), if we choose m = 1/2 . The second-order Casimir operator of OSp(4|2) = D(2, 1; − 1 2 ) is defined by the following expression [32,18,20]…”

Section: Superconformal Symmetry Of the Spectrumsupporting

confidence: 76%

“…The generators (4.22) and (4.23) will go over to the trigonometric realization of the OSp(4|2) generators given in [24], if we pass to the case without spin degrees of freedom. Note that the spectrum and the energy of the vacuum states in the models of the D(2, 1; α) superconformal mechanics is known to exhibit an explicit dependence on α [19,24]. The vacuum energy of the "conformal" Hamiltonian (4.28) including the case of q = 0 is also defined by the expression (3.30).…”

Section: Superconformal Symmetry Of the Spectrummentioning

confidence: 99%

“…[17,18,19,20] to the case of non-zero mass. On the other hand, in the papers [21,22,23,24] (see also [25,26]) there were found different realizations of N = 4, d = 1 superconformal groups and established some relations between the deformed supersymmetries and superconformal symmetries. One of the purposes of our paper is to clarify the role of the deformed SU(2|1) supersymmetry and its superconformal extension in the quantum spectrum of the systems with semi-dynamical variables.…”

Section: Introductionmentioning

confidence: 99%

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Deformed supersymmetric quantum mechanics with spin variables

Fedoruk¹,

Ivanov²,

Sidorov³

2018

J. High Energ. Phys.

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Abstract:We quantize the one-particle model of the SU(2|1) supersymmetric multiparticle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the massdimension deformation parameter m and SU(2) spin q ∈ Z >0 , 1/2 + Z 0 . It is found that the states at the fixed energy level form irreducible multiplets of the supergroup SU(2|1) . Also, the hidden superconformal symmetry OSp(4|2) of the model is revealed in the classical and quantum cases. We calculate the OSp(4|2) Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed q are unified into an irreducible OSp(4|2) multiplet.

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Section: Superconformal Symmetry Of the Spectrumsupporting

confidence: 76%

Section: Superconformal Symmetry Of the Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deformed supersymmetric quantum mechanics with spin variables

Fedoruk¹,

Ivanov²,

Sidorov³

2018

J. High Energ. Phys.

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“…The remaining generators entering table (34) and their (anti)commutators defining G con f are recovered from repeated (anti)commutators involving the operators Q 10 , Q 01 and K .…”

Section: The Dressed Multipletsmentioning

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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$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$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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“…Thus the generators (Q, S, H, D, K) form the osp(1|2) super Lie algebra (see, e.g., [36,37]), i.e. the super-extension of the conformal algebra so(2, 1) in one dimension.…”

Section: From Bulk Supersymmetry To Osp(1|2) Superconformal Symmetry mentioning

confidence: 99%

Supersymmetric Liouville theory in AdS2 and AdS/CFT

Beccaria

Jiang

Tseytlin

2019

J. High Energ. Phys.

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In a series of recent papers, a special kind of AdS 2 /CFT 1 duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS 2 background are the same as the correlators of the corresponding primary operators in the chiral half of that 2d CFT in flat space restricted to the real line. The examples considered were: (i) the Liouville theory where the operator dual to the Liouville scalar in AdS 2 is the stress tensor; (ii) the abelian Toda theory where the operators dual to the Toda scalars are the W-algebra generators; (iii) the non-abelian Toda theory where the Liouville field is dual to the stress tensor while the extra gauged WZW theory scalars are dual to non-abelian parafermionic operators. By direct Witten diagram computations in AdS 2 one can check that the structure of the boundary correlators is indeed consistent with the Virasoro (or higher) symmetry. Here we consider a supersymmetric generalization: the N = 1 superconformal Liouville theory in AdS 2 . We start with the super Liouville theory coupled to 2d supergravity and show that a consistent restriction to rigid AdS 2 background requires a non-zero value of the supergravity auxiliary field and thus a modification of the Liouville potential from its familiar flat-space form. We show that the Liouville scalar and its fermionic partner are dual to the chiral half of the stress tensor and the supercurrent of the super Liouville theory on the plane. We perform tests supporting the duality by explicitly computing AdS 2 Witten diagrams with bosonic and fermionic loops.Recent investigations of correlators of operators on 1/2 BPS Wilson loop at strong coupling using AdS 5 × S 5 superstring action (see [1,2] and refs. there) motivate the study of boundary correlators in conformal quantum field theories in AdS 2 space. While for a general QFT in AdS 2 one expects the boundary correlators to be covariant under the isometry of AdS 2 or the 1d conformal group SO(2, 1),

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From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(

Cited by 17 publications

References 58 publications

Deformed supersymmetric quantum mechanics with spin variables

Deformed supersymmetric quantum mechanics with spin variables

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

Supersymmetric Liouville theory in AdS2 and AdS/CFT

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