On the four-dimensional holoraumy of the 4D, 𝒩 = 1 complex linear supermultiplet

Caldwell, W. I.; Diaz, Alejandro N.; Friend, Isaac; Gates, S. James; Harmalkar, Siddhartha; Lambert-Brown, Tamar; Lay, David C.; Martirosova, Karina; Meszaros, Victor A.; Omokanwaye, Mayowa; Rudman, Shaina; Shin, Daeljuck; Vershov, Anthony

doi:10.1142/s0217751x18500720

Cited by 12 publications

(23 citation statements)

References 23 publications

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“…A major purpose of this current work is to "flesh out" (i. e. present explicit results) the assertions made in writing (3.1). As our previous discussions of 4D holoraumy were in the context of N = 1 supermultiplets [27,28], the quantities S i j perforce vanish. Thus, the work that follows provides the first opportunity to realize these more general structures by working out details within the context of a specific set of examples.…”

Section: )mentioning

confidence: 58%

“…In previous work [28], an observation was introduced into the literature about 4D, N = 1 minimal off-shell supermultiplets. Namely, when one determines the lattice parameters Π = (p, q, r, s) associated with each supermultiplet via a holoraumy calculation one is led to the function 1) and the values of the lattice parameters are shown in Figure 5.…”

Section: Resultsmentioning

confidence: 99%

“…The "isospin" index i takes on values 1 and 2. As in previous works [27,28] we introduce a 4D supermultiplet "representation index" ( R) that takes on the values of ( 2VS), ( 2TS), ( 2AVS), and ( 2ATS). This allows us to express the four spinors shown in (4.2) collectively as Ψ ( R) ci and we are now in position to state the main results of this investigation to calculate its fermionic holoraumy.…”

Section: D N = 2 Supermultipletmentioning

confidence: 99%

“…Adinkras are one dimensional graphical representations [20,21,22,23,24] of the garden algebras and by their study has led to the concept of holoraumy [25,26] as a tool for this purpose. However, the concept of holoraumy possesses a natural extension from the context of 1D SUSY systems to higher dimensional ones and in particular to 4D SUSY representations [27,28]. So our proposition is the data normally accessed in Lie algebra (via use of eigenvectors and eigenvalues) within the context of spacetime SUSY theories is accessed via the holoraumy.…”

Section: Introductionmentioning

confidence: 99%

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Examples of 4D, 𝒩 = 2 holoraumy

Gates¹,

Mak

2019

Int. J. Mod. Phys. A

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We provide an introduction to the concepts of Holoraumy tensors, Lorentz covariant four-dimensional "Gadgets", and Gadget angles within the context of minimal off-shell 4D, N = 2 supermultiplets. This is followed by the calculation of the Holoraumy tensors, Gadgets, and Gadget angles for minimal off-shell supermultiplets. Four tetrahedrons in four 3D subspaces of the Holoraumy lattice space are found.

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Section: )mentioning

confidence: 58%

Section: Resultsmentioning

confidence: 99%

Section: D N = 2 Supermultipletmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Examples of 4D, 𝒩 = 2 holoraumy

Gates¹,

Mak

2019

Int. J. Mod. Phys. A

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“…(b.) This general behavior can be seen in all off-shell holoraumy calculations in 4D, N = 1 supermultiplets[2].(c.) The final portion to seeing the role the duality rotations play emerges from understanding how superspace Lagrangians describe dynamical systems.…”

mentioning

confidence: 55%

On the ubiquity of electromagnetic-duality rotations in 4D, 𝒩 = 1 holoraumy tensors for on-shell 4D supermultiplets

Gates

Lay

Mak

et al. 2020

Int. J. Mod. Phys. A

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Holoraumy is a tool being developed for dimensional enhancement (supersymmetry holography) where the goal is to build higher dimensional supersymmetric multiplets from lower dimensional supersymmetric multiplets. In this paper, for the first time we investigate holoraumy for on-shell supersymmetry. Specifically, the holoraumy tensors for a number of familiar 4D, N = 1 multiplets are calculated. It is shown in all of these cases of on-shell theories, the holoraumy is of the form of an electromagnetic duality charge multiplying a composite transformation involving an electromagnetic duality rotation through an angle of π/2 times a space time translation. The details of our calculations can be found at the HEPTHools Data Repository.

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Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces

Gates¹,

Hu²,

Mak³

2020

J. High Energ. Phys.

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The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in the $$ \mathcal{N} $$ N = 1, $$ \mathcal{N} $$ N = 2A, and $$ \mathcal{N} $$ N = 2B unconstrained scalar 10D superfields are presented. These are made possible by a discovery of the dependence of the superfield component expansion on the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). A consequential deliverable of this advance is it provides the first explicit, in terms of component fields, examples of all the off-shell 10D Nordström SG theories relevant to string theory, without off-shell central charges that are reducible but with finite numbers of fields. An analogue of Breitenlohner’s approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the superconformal prepotential superfields of 10D off-shell supergravity theories and Yang-Mills theories.

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On the four-dimensional holoraumy of the 4D, 𝒩 = 1 complex linear supermultiplet

Cited by 12 publications

References 23 publications

Examples of 4D, 𝒩 = 2 holoraumy

Examples of 4D, 𝒩 = 2 holoraumy

On the ubiquity of electromagnetic-duality rotations in 4D, 𝒩 = 1 holoraumy tensors for on-shell 4D supermultiplets

Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces

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