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’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, <inline-formula> <math display="inline"&...
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Online Access: | https://www.mdpi.com/2073-8994/11/2/217 |
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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’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, <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’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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>20</mn> <mspace width="3.33333pt"></mspace> <mo>×</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’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, <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’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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>20</mn> <mspace width="3.33333pt"></mspace> <mo>×</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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