Frames for Supersymmetry

Doran, Charles F.; Faux, Michael; Gates, S. James; Hübsch, Tristan; Iga, Kevin; Landweber, Gregory D.

doi:10.1142/s0217751x09044644

Cited by 17 publications

(50 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years the structure of its linear representations has been unveiled by a series of works (upon which the present investigation is based) [2]- [13], that we will briefly comment. The linear representations under considerations (supermultiplets) contain a finite, equal number of bosonic and fermionic fields depending on a single coordinate (the time).…”

Section: Introductionmentioning

confidence: 99%

“…The linear representations are characterized by a series of properties which, for sake of consistency, are reviewed in Appendix A. They include the grading of the fields (in physical terms, their mass-dimension), the length and the field content of the supermultiplets [2,4], the dressing transformations [14,15,2], the association with graphs [3,5,6,9,10,11], the connectivity symbol [9,10] characterizing inequivalent representation with a given field content (the notion of inequivalent representations has been discussed in [5,6]), the mirror duality [8], etc.…”

Section: Introductionmentioning

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%

“…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%

“…† A fermionic source [5,6,9] is a fermionic Setting (10) is not something innocuous. One has in fact to guarantee that the resulting action, after the "renaming" of the fields, is still N = 4-invariant.…”

Section: Introductionmentioning

confidence: 99%

See 4 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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…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%

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

View full text Add to dashboard Cite

show abstract

One-Dimensional Structures Behind Twisted and Untwisted SuperYang–Mills Theory

Baulieu

Toppan²

2011

Lett Math Phys

View full text Add to dashboard Cite

We give a one-dimensional interpretation of the four-dimensional twisted N = 1 superYangMills theory on a Kähler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 superYang-Mills theory.

show abstract

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

Carvalho¹,

Kuznetsova²,

Toppan³

2010

Nuclear Physics B

View full text Add to dashboard Cite

We discuss four off-shell N = 4 D = 1 supersymmetry transformations, their associated one-dimensional σ-models and their mutual relations. They are given by I) the (4, 4) lin linear "root" supermultiplet (supersymmetric extension of R 4 ), II) the (3, 4, 1) lin linear supermultiplet (supersymmetric extension of R 3 ), III) the (3, 4, 1) nl non-linear supermultiplet living on S 3 and IV) the (2, 4, 2) nl non-linear supermultiplet living on S 2 . The I → II map is the supersymmetric extension of the R 4 → R 3 bilinear map, while the II → IV map is the supersymmetric extension of the S 3 → S 2 first Hopf fibration. The restrictions on the S 3 , S 2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content.The σ-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential.The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched.Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N ≤ 8.

show abstract

Frames for Supersymmetry

Cited by 17 publications

References 5 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

One-Dimensional Structures Behind Twisted and Untwisted SuperYang–Mills Theory

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

Contact Info

Product

Resources

About