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Symmetry 2019, 11(2), 217; https://doi.org/10.3390/sym11020217

4D, N = 1 Matter Gravitino Genomics

Department of Physics, Brown University, Box 1843, 182 Hope Street, Providence, RI 02912, USA
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Received: 21 December 2018 / Revised: 21 January 2019 / Accepted: 6 February 2019 / Published: 13 February 2019
(This article belongs to the Special Issue Supersymmetric Field Theory 2018)
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Abstract

Adinkras are graphs that encode a supersymmetric representation’s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry “genomics” project is to classify all 4D, N = 1 off-shell supermultiplets in terms of their adinkras. In previous works, the genomics project uncovered two fundamental isomer adinkras, the cis- and trans-adinkras, into which all multiplets investigated to date can be decomposed. The number of cis- and trans-adinkras describing a given multiplet define the isomer-equivalence class to which the multiplet belongs. A further refining classification is that of a supersymmetric multiplet’s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet’s holoraumy defines the multiplet’s holoraumy-equivalence class. Together, a multiplet’s isomer-equivalence and holoraumy-equivalence classes are two of the main characteristics used to distinguish the adinkras associated with different supersymmetry multiplets in higher dimensions. This paper focuses on two matter gravitino formulations, each with 20 bosonic and 20 fermionic off-shell degrees of freedom, analyzes them in terms of their isomer- and holoraumy-equivalence classes, and compares with non-minimal supergravity which is also a 20 × 20 multiplet. This analysis fills a missing piece in the supersymmetry genomics project, as now the isomer-equivalence and holoraumy-equivalence for representations up to spin two in component fields have been analyzed for 4D, N = 1 supersymmetry. To handle the calculations of this research effort, we have used the Mathematica software package called Adinkra.m. This package is open-source and available for download at a GitHub Repository. Data files associated with this paper are also published open-source at a Data Repository also on GitHub. View Full-Text
Keywords: adinkras; equivalence classes; field theory; genomics; holography; holoraumy; representation theory; supersymmetry adinkras; equivalence classes; field theory; genomics; holography; holoraumy; representation theory; supersymmetry
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Mak, S.-N.H.; Stiffler, K. 4D, N = 1 Matter Gravitino Genomics. Symmetry 2019, 11, 217.

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