A canticle on (4,0) supergravity-scalar multiplet systems for a “cognoscente”

Dhanawittayapol, Rujikorn; Gates, S. James; Rana, Lubna

doi:10.1016/s0370-2693(96)01254-3

Cited by 14 publications

(13 citation statements)

References 12 publications

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“…For example, the four off-shell supermultiplets of worldsheet (4, 0)-supersymmetry examined in Ref. [29] are all valises; they conform to our criterion straightforwardly, since these models exhibit unidextrous (chiral) supersymmetry, wherein no "ambidextrous 2-color bow-tie" obstruction ( 14) can exist. Evidently, this implies:…”

Section: Corollary 21 (Extension Obstruction)mentioning

confidence: 59%

See 1 more Smart Citation

On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets

Gates,

Hubsch

2011

Preprint

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There exist myriads of off-shell worldline supermultiplets for (N ≤ 32)-extended supersymmetry in which every supercharge maps a component field to precisely one other component field or its derivative. A subset of these extends to off-shell worldsheet (p, q)-supersymmetry and is characterized by the twin theorems 2.1 and 2.2 in this note. The evasion of the obstruction defined in these theorems is conjectured to be sufficient for a worldline supermultiplet to extend to worldsheet supersymmetry; it is also a necessary filter for dimensional extension to higher-dimensional spacetime. We show explicitly how to "re-engineer" an Adinkra-if permitted by the twin theorems 2.1 and 2.2-so as to depict an off-shell supermultiplet of worldsheet (p, q)supersymmetry.

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Section: Corollary 21 (Extension Obstruction)mentioning

confidence: 59%

“…Of course, worldsheet supersymmetry is also important in its own right [22,23,24,25] and affords comparison with numerous known results; see Refs. [26,27,28,2,5,29,30,31,32,33,34], to name but a few.…”

Section: Introduction Results and Summarymentioning

confidence: 99%

On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets

Gates,

Hubsch

2011

Preprint

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“…Worldsheet dimensional extension is thus a stepping stone towards dimensional extension to higher-dimensional spacetimes. Of course, worldsheet supersymmetry is also important in its own right [23][24][25][26] and affords comparison with numerous known results; see [2,5,[27][28][29][30][31][32][33][34][35], to name but a few.…”

Section: Introduction Results and Summarymentioning

confidence: 99%

“…Each closed path depicts a closed D-orbit 5 , so that the sum of height-weighted spins along a closed path is the trace of the height-weighted Spin(1, 1)-action over the given closed D-orbit. 5 An orbit generated by a sequential application of superderivatives is considered closed it if returns to a constant multiple of a ∂ For example, the four off-shell supermultiplets of worldsheet (4, 0)-supersymmetry examined in [30] are all valises; they conform to our criterion straightforwardly, since these models exhibit unidextrous (chiral) supersymmetry, wherein no "ambidextrous two-color bow-tie" obstruction (2.6) can exist.…”

Section: Sylvester J Gates Jr and Tristan Hübschmentioning

confidence: 99%

On dimensional extension of supersymmetry: from worldlines to worldsheets

Gates

Hübsch

2012

Advances in Theoretical and Mathematical Physics

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There exist myriads of off-shell worldline supermultiplets for (N ≤ 32)-extended supersymmetry in which every supercharge maps a component field to precisely one other component field or its derivative. A subset of these extends to off-shell worldsheet (p, q)-supersymmetry, and is characterized herein by evading an obstruction specified visually and computationally by the "bow-tie" and "spin sum rule" twin theorems. The evasion of this obstruction is proven to be both necessary and sufficient for a worldline supermultiplet to extend to worldsheet supersymmetry; it is also a necessary filter for dimensional extension to higher-dimensional spacetime. We show explicitly how to "re-engineer" an Adinkra-if permitted by the twin theorems-so as to depict an off-shell supermultiplet of worldsheet (p, q)-supersymmetry. This entails starting from an Adinkra depicting a specific type of supermultiplet of worldline (p+q)-supersymmetry, judiciously re-defining a subset of component fields and e-print archive: http://lanl.arXiv.org/abs/1104.0722v2

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“…Many years ago [57,58], it was demonstrated that there is a minimum of four distinct (4, 0) valise supermultiplets each containing four bosons and four fermions. Thus, one can introduce a "representation label" (R), which takes on four values denoted by SM-I, SM-II, SM-III, and SM-IV.…”

Section: Reviewing the Known 2d N = (4 0) Minimal Scalar Valise Supmentioning

confidence: 99%

Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into ℓ- and ℓ ˜ -Equivalence Classes

et al. 2019

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Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of B C 3 , the signed permutation group of three elements, and B C 4 , the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via B C 4 boson × B C 3 color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the gadget, which is used to distinguish adinkras. We show how 96 equivalence classes of adinkras that are based on the gadget emerge in terms of B C 3 and B C 4 . We also comment on the importance of the gadget as it relates to separating out dynamics in terms of Kähler-like potentials. Thus, on the basis of the complete analysis of the supersymmetrical representations achieved in the preparatory first four sections, the final comprehensive achievement of this work is the construction of the universal B C 4 non-linear σ -model.

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A canticle on (4,0) supergravity-scalar multiplet systems for a “cognoscente”

Cited by 14 publications

References 12 publications

On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets

On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets

On dimensional extension of supersymmetry: from worldlines to worldsheets

Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into ℓ- and ℓ ˜ -Equivalence Classes

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