Symplectic sigma models in superspace

Ivanov, E.; Smilga, Andrei

doi:10.1016/j.nuclphysb.2004.05.006

Cited by 23 publications

(37 citation statements)

References 23 publications

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“…The pseudo-Hermitian property of the Hamiltonian (called "cryptoreality" in Ref. 33) was discussed [34][35][36][37] in terms of the conjugation transformationĤ = e R He −R relating the pseudo-Hermitian Hamiltonian H to its self-adjointH counterpart. In Ref.…”

Section: Discussionmentioning

confidence: 99%

On Supergroups With Odd Clifford Parameters and Supersymmetry With Modified Leibniz Rule

Kuznetsova

Rojas²,

Toppan³

2008

Int. J. Mod. Phys. A

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We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with nonanticommutative supersymmetry is discussed. A Berezinlike calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest nontrivial example is given by the N = 2 supersymmetric quantum mechanics with a real (1, 2, 1) multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender-Boettcher pseudo-Hermitian Hamiltonian is encountered when solving the equations of motions of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.

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Section: Discussionmentioning

confidence: 99%

On Supergroups With Odd Clifford Parameters and Supersymmetry With Modified Leibniz Rule

Kuznetsova

Rojas²,

Toppan³

2008

Int. J. Mod. Phys. A

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“…Finally, we would like to point out that the general N=4 superfield action for the N=8 multiplet (5,8,3) in the splitting (3, 4, 1) ⊕ (2, 4, 2) was constructed previously and studied in [21,22,24]. At the same time, the alternative splitting (4, 4, 0) ⊕ (3, 4, 1) was not elaborated on too much.…”

Section: Potential Termsmentioning

confidence: 95%

Hierarchy of mechanics models

Ivanov¹,

Lechtenfeld

Sutulin³

2008

Nuclear Physics B

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Using the N =4 superspace approach in one dimension (time), we construct general N =8 supersymmetric mechanics actions for the multiplets (b, 8, 8−b) classified in hep-th/0406015, with the main focus on the previously unexplored cases of (8, 8, 0), (7, 8, 1) and (6, 8, 2) , as well as on (5, 8, 3) for completeness. N =8 supersymmetry of the action amounts to a harmonicity condition for the Lagrangian with respect to its superfield arguments. We derive the generic off-shell component action for the "root" multiplet (8,8, 0), prove that the actions for all other multiplets follow from it through automorphic dualities and argue that this hierarchical structure is universal. The bosonic target geometry in all cases is conformally flat, with a unique scalar potential (except for the root multiplet). We show that the N =4 superfield constraints respect the full R-symmetry and find the explicit realization of its quotient over the manifest R-symmetry on superfields and component fields. Several R-symmetric N =4 superfield Lagrangians with N =8 supersymmetry are either newly found or reproduced by a simple universal method.

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“…It still remains to be understood how they are related to multiplets with an infinite number of auxiliary fields, which naturally appear in various versions of harmonic N=8, d=1 superspace (see e.g. [34,38,35]). Also, the relevance of the latter to the N=8 SQM model building needs to be explored further.…”

Section: N=8 Supermultipletsmentioning

confidence: 99%

ABC of supermultiplets

Bellucci

Ivanov²,

Krivonos³

et al. 2004

Nuclear Physics B

194

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We construct a variety of off-shell N =8, d=1 supermultiplets with finite numbers of component fields as direct sums of properly constrained N =4, d=1 superfields. We also show how these multiplets can be described in N =8, d=1 superspace where the whole amount of supersymmetry is manifest. Some of these multiplets can be obtained by dimensional reduction from N =2 multiplets in d=4, whereas others cannot. We give examples of invariant superfield actions for the multiplets constructed, including N =8 superconformally invariant ones.

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Symplectic sigma models in superspace

Cited by 23 publications

References 23 publications

On Supergroups With Odd Clifford Parameters and Supersymmetry With Modified Leibniz Rule

On Supergroups With Odd Clifford Parameters and Supersymmetry With Modified Leibniz Rule

Hierarchy of mechanics models

ABC of supermultiplets

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