4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics

Adinkras are graphs that encode a supersymmetric representation&#8217;s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry &#8220;genomics&#8222; project is to classify all 4D, <inline-formula> <math display="inline"&...

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Main Authors: S.-N. Hazel Mak, Kory Stiffler
Format: Article
Language:English
Published: MDPI AG 2019-02-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/11/2/217
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spelling doaj-da49df7acb5a47069e57100708abb93b2020-11-24T21:16:00ZengMDPI AGSymmetry2073-89942019-02-0111221710.3390/sym11020217sym110202174D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino GenomicsS.-N. Hazel Mak0Kory Stiffler1Department of Physics, Brown University, Box 1843, 182 Hope Street, Providence, RI 02912, USADepartment of Physics, Brown University, Box 1843, 182 Hope Street, Providence, RI 02912, USAAdinkras are graphs that encode a supersymmetric representation&#8217;s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry &#8220;genomics&#8222; project is to classify all 4D, <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> 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&#8217;s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet&#8217;s holoraumy defines the multiplet&#8217;s holoraumy-equivalence class. Together, a multiplet&#8217;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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>20</mn> <mspace width="3.33333pt"></mspace> <mo>&#215;</mo> <mspace width="3.33333pt"></mspace> <mn>20</mn> </mrow> </semantics> </math> </inline-formula> 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, <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> supersymmetry. To handle the calculations of this research effort, we have used the <i>Mathematica</i> software package called <i>Adinkra.m</i>. This package is open-source and available for download at a <i>GitHub</i> Repository. Data files associated with this paper are also published open-source at a Data Repository also on <i>GitHub</i>.https://www.mdpi.com/2073-8994/11/2/217adinkrasequivalence classesfield theorygenomicsholographyholoraumyrepresentation theorysupersymmetry
collection DOAJ
language English
format Article
sources DOAJ
author S.-N. Hazel Mak
Kory Stiffler
spellingShingle S.-N. Hazel Mak
Kory Stiffler
4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
Symmetry
adinkras
equivalence classes
field theory
genomics
holography
holoraumy
representation theory
supersymmetry
author_facet S.-N. Hazel Mak
Kory Stiffler
author_sort S.-N. Hazel Mak
title 4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
title_short 4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
title_full 4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
title_fullStr 4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
title_full_unstemmed 4D, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Matter Gravitino Genomics
title_sort 4d, <inline-formula> <mml:math id="mm999" display="block"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> matter gravitino genomics
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-02-01
description Adinkras are graphs that encode a supersymmetric representation&#8217;s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry &#8220;genomics&#8222; project is to classify all 4D, <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> 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&#8217;s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet&#8217;s holoraumy defines the multiplet&#8217;s holoraumy-equivalence class. Together, a multiplet&#8217;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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>20</mn> <mspace width="3.33333pt"></mspace> <mo>&#215;</mo> <mspace width="3.33333pt"></mspace> <mn>20</mn> </mrow> </semantics> </math> </inline-formula> 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, <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> supersymmetry. To handle the calculations of this research effort, we have used the <i>Mathematica</i> software package called <i>Adinkra.m</i>. This package is open-source and available for download at a <i>GitHub</i> Repository. Data files associated with this paper are also published open-source at a Data Repository also on <i>GitHub</i>.
topic adinkras
equivalence classes
field theory
genomics
holography
holoraumy
representation theory
supersymmetry
url https://www.mdpi.com/2073-8994/11/2/217
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