Refining the Classification of the Irreps of the 1d N-Extended Supersymmetry

Kuznetsova, Z.; Toppan, Francesco

doi:10.1142/s0217732308023761

Cited by 41 publications

(94 citation statements)

References 9 publications

(49 reference statements)

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“…In this spirit, the authors of [9][10][11][12][13][14][15] developed a detailed classification of a huge class (∼ 10 12 for no more than 32 supersymmetries) of worldline supermultiplets wherein each supercharge maps each component field to precisely one other component field or its derivative, and which are faithfully represented by graphs called Adinkras; see also [16][17][18][19][20][21][22]. The subsequently intended dimensional extension has been addressed recently [7,8], and the purpose of the present note is to complement this effort and identify an easily verifiable obstruction to dimensional extension.…”

Section: Introduction Results and Summarymentioning

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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Section: Introduction Results and Summarymentioning

confidence: 99%

On dimensional extension of supersymmetry: from worldlines to worldsheets

Gates

Hübsch

2012

Advances in Theoretical and Mathematical Physics

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“…Let us consider a D-module irrep of a N -extended superconformal algebra (for our purposes N = 1, 2, 4, 8) acting on a (k, N , N − k) supermultiplet [29,30,31,32] (namely, k propagating bosons, N fermions and N − k bosonic auxiliary fields). In the linear basis the propagating bosons are labeled as x 1 , ..., x k , the fermions as ψ 1 , ..., ψ N and the auxiliary bosons as b 1 , ..., b N −k .…”

Section: Introductionmentioning

confidence: 99%

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
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In this paper we quantize superconformal σ-models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a DFF term, are considered. Without a DFF term (Calogero potential only) the supersymmetry is unbroken. The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory.Besides the osp(1|2) examples, we explicitly quantize the superconformally-invariant worldine σ-models defined by the N = 4 (1, 4, 3) supermultiplet (with D(2, 1; α) invariance, for α = 0, −1) and by the N = 2 (2, 2, 0) supermultiplet (with two-dimensional target and sl(2|1) invariance). The parameter α is the scaling dimension of the (1, 4, 3) supermultiplet and, in the DFF case, has a direct interpretation as a vacuum energy. In the DFF case, for the sl(2|1) models, the scaling dimension λ is quantized (either λ = 1 2 + Z or λ = Z). The ordinary two-dimensional oscillator is recovered, after imposing a superselection restriction, from the λ = − 1 2 model. In particular a single bosonic vacuum is selected. The spectrum of the unrestricted two-dimensional theory is decomposed into an infinite set of lowest weight representations of sl(2|1). Extra fermionic raising operators, not belonging to the original sl(2|1) superalgebra, allow (for λ = 1 2 + Z) to construct the whole spectrum from the two degenerate (one bosonic and one fermionic) vacua.

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“…The former approach obviously will contain remnants of information about the symmetries of the higher dimensional spacetime. How are these data "downloaded" onto the theories constructed from a purely adinkra network-based [1,2,3,4,5,6,7,8,9,10] approach?…”

Section: Introductionmentioning

confidence: 99%

Adinkras, 0-branes, holoraumy and the SUSY QFT/QM correspondence

Calkins

Gates

et al. 2015

Int. J. Mod. Phys. A

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We propose the recently defined "Holoraumy Tensor" to play a critical role in defining a metric to establish a correspondence between 4D, [Formula: see text]-extended 0-brane-based valise supermultiplet representations and, correspondingly via "SUSY Holography," on the space of 1D, N-extended network-based adinkras. Using an analogy with the su(3) algebra, it is argued the 0-brane holoraumy tensors play the role of the " d -coefficients" and provide a newly established tool for investigating supersymmetric representation theory.

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Refining the Classification of the Irreps of the 1d N-Extended Supersymmetry

Cited by 41 publications

References 9 publications

On dimensional extension of supersymmetry: from worldlines to worldsheets

On dimensional extension of supersymmetry: from worldlines to worldsheets

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
View full text Add to dashboard Cite

Adinkras, 0-branes, holoraumy and the SUSY QFT/QM correspondence

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Refining the Classification of the Irreps of the 1d N-Extended Supersymmetry

Cited by 41 publications

References 9 publications

On dimensional extension of supersymmetry: from worldlines to worldsheets

On dimensional extension of supersymmetry: from worldlines to worldsheets

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(Cunha1, Holanda2, Toppan3 2017Phys. Rev. D162100View full textAdd to dashboardCite

Adinkras, 0-branes, holoraumy and the SUSY QFT/QM correspondence

Contact Info

Product

Resources

About

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
View full text Add to dashboard Cite