Supersymmetric extension of Hopf maps: σ-models and the fibration

Carvalho, L. Faria; Kuznetsova, Z.; Toppan, Francesco

doi:10.1016/j.nuclphysb.2010.03.017

Cited by 10 publications

(13 citation statements)

References 60 publications

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“…The determination of the Schur's property of higherlength supermultiplets requires the compatibility with the dressing (this implies that the most general commuting matrix of the root supermultiplet is restricted by the further requirement of commuting with the dressing matrix D discussed in Appendix A). The analysis for the minimal supermultiplets has been presented in [17]. We extend here the investigation of [17] Without loss of generality we can work with the conventions of Appendix B.…”

Section: Connectivity Symbol Of the N = 4 Fully Reducible Representatmentioning

confidence: 99%

“…Non-minimal linear representations have been discussed in [4,12,13,16,17]. The maximal finite number n max of bosonic (fermionic) fields entering a non-minimal representation is given by [12,13] n max = 2 N −1 .…”

Section: Introductionmentioning

confidence: 99%

“…This Section applies the methods presented in [17] where, for the minimal supermultiplets, the supersymmetric extension of the Schur's lemma was constructed.…”

Section: Introductionmentioning

confidence: 99%

“…1D supersymmetric σ-models were first discussed in [19,20]; minimal N = 4 σ-models were constructed in [21]- [26], while minimal N = 8-invariant σ-models were investigated in [27]. There are also supersymmetric σ-models based on non-linear realizations of the supersymmetry that we are not discussing here (for a partial list of references one can consult [17]). …”

Section: Introductionmentioning

confidence: 99%

“…, k) of lower-dimension in a supermultiplet can be assumed [4] to be bosonic and have 0-mass dimension. They are physically interpreted [7,28,17] as the target-coordinates of the associated σ-model. An N = 4-invariant off-shell action S, with the correct dimension of a kinetic term, is obtained [4,7,28,17] through…”

Section: Introductionmentioning

confidence: 99%

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On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

Gonzales¹,

Khodaee²,

Toppan³

2011

Journal of Mathematical Physics

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We construct the non-minimal linear representations of the N = 4 Extended Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N = 5 linear representations is given. Two types of N = 4 σ-models based on non-minimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained prepotential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories.

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Section: Connectivity Symbol Of the N = 4 Fully Reducible Representatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This Section applies the methods presented in [17] where, for the minimal supermultiplets, the supersymmetric extension of the Schur's lemma was constructed.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

Gonzales¹,

Khodaee²,

Toppan³

2011

Journal of Mathematical Physics

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Graded Hopf maps and fuzzy superspheres

Hasebe

2011

Nuclear Physics B

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We argue supersymmetric generalizations of fuzzy two-and four-spheres based on the unitary-orthosymplectic algebras, uosp(N |2) and uosp(N |4), respectively. Supersymmetric version of Schwinger construction is applied to derive graded fully symmetric representation for fuzzy superspheres. As a classical counterpart of fuzzy superspheres, graded versions of 1st and 2nd Hopf maps are introduced, and their basic geometrical structures are studied. It is shown that fuzzy superspheres are represented as a "superposition" of fuzzy superspheres with lower supersymmetries. We also investigate algebraic structures of fuzzy two-and four-superspheres to identify su(2|N ) and su(4|N ) as their enhanced algebraic structures, respectively. Evaluation of correlation functions manifests such enhanced structure as quantum fluctuations of fuzzy supersphere.

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Pure and entangled ${\cal N}=4$N=4 linear supermultiplets and their one-dimensional sigma-models

Gonzales

Iga

Khodaee

et al. 2012

Journal of Mathematical Physics

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Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N = 4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs are known as "Adinkras").We further prove the existence of "entangled" linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N = 4 supermultiplet with field content (3,8,5). It interpolates between two inequivalent pure N = 4 supermultiplets with the same field content. The one-dimensional N = 4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented.The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed.Discrete properties such as "chirality" and "coloring" can discriminate different supermultiplets. The tools used in our classification include, among others, the notion of field content, connectivity symbol, commuting group, node choice group and so on.In this paper we present, for N = 4, the classification of the homogeneous (minimal and nonminimal) linear pure supermultiplets of the global N -extended one-dimensional Supersymmetry Algebra (the dynamical Lie superalgebra of the Supersymmetric Quantum Mechanics [1])A pure supermultiplet admits at least one graphical presentation (the corresponding graph is known as "Adinkra", [2]). We further prove the existence of the conjectured non-adinkrizable supermultiplets [3] (we prefer to call them here"entangled supermultiplets") which do not admit a graphical presentation, by explicitly introducing a supermultiplet, proved to be entangled, which interpolates between two pure supermultiplets (the interpolation is measured by an angle).We also construct a one-dimensional N = 4 supersymmetric σ-model with three target coordinates, defined in terms of the given entangled supermultiplet.This work is based on several advances, made in the course of the last decade, concerning the classification of homogeneous linear supermultiplets of the one-dimensional (1) N -extended superalgebra [4]- [19]. The classification of the N = 4 pure supermultiplets is made possible by combining different tools introduced in several works [11]-[18]. These tools (which include, among others, the notions of engineering dimension, length of a supermultiplet, mirror symmetry duality, connectivity symbol, node choice group, commuting group, possible chirality and/or coloring of the supermultiplets) are revised in an Appendix and further discussed in the text, when needed.A key issue concerns the distinction between the equivalence class of pure supermultiplets and the equivalence class of their associated graphs (we recall that fields are represented by vertices, while supersymmetry transformations are represented by colored edges, solid or dashed according to their sign, see the Appendix). Equivalent graphs are related by two types of moves: i) local moves, ba...

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Supersymmetric extension of Hopf maps: σ-models and the fibration

Cited by 10 publications

References 60 publications

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

On nonminimal ${\cal N}=4$N=4 supermultiplets in 1D and their associated σ-models

Graded Hopf maps and fuzzy superspheres

Pure and entangled ${\cal N}=4$N=4 linear supermultiplets and their one-dimensional sigma-models

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