Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy
We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of (N,N) supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construc...
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Інститут математики НАН України
2010
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146346 |
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| Zitieren: | Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy / D.M. Schmidtt // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 24 назв. — англ. |
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irk-123456789-1463462019-02-10T01:23:19Z Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy Schmidtt, D.M. We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of (N,N) supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construction is based on an extended Riemann-Hilbert problem for affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic-like fermionic local current identities is introduced and it is shown that the simplest one, corresponding to the lowest isospectral times t₊₋₁ provides the supercharges generating rigid supersymmetry transformations in 2D superspace. The number of supercharges is equal to the dimension of the fermionic kernel of a given semisimple element E ∈ g which defines both, the physical degrees of freedom and the symmetries of the model. The general construction is applied to the N=(1,1) and N=(2,2) sinh-Gordon models which are worked out in detail. Remove selected 2010 Article Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy / D.M. Schmidtt // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T60; 37K20; 37K10 DOI:10.3842/SIGMA.2010.043 http://dspace.nbuv.gov.ua/handle/123456789/146346 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of (N,N) supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construction is based on an extended Riemann-Hilbert problem for affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic-like fermionic local current identities is introduced and it is shown that the simplest one, corresponding to the lowest isospectral times t₊₋₁ provides the supercharges generating rigid supersymmetry transformations in 2D superspace. The number of supercharges is equal to the dimension of the fermionic kernel of a given semisimple element E ∈ g which defines both, the physical degrees of freedom and the symmetries of the model. The general construction is applied to the N=(1,1) and N=(2,2) sinh-Gordon models which are worked out in detail.
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| format |
Article |
| author |
Schmidtt, D.M. |
| spellingShingle |
Schmidtt, D.M. Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schmidtt, D.M. |
| author_sort |
Schmidtt, D.M. |
| title |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy |
| title_short |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy |
| title_full |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy |
| title_fullStr |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy |
| title_full_unstemmed |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy |
| title_sort |
supersymmetry of affine toda models as fermionic symmetry flows of the extended mkdv hierarchy |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146346 |
| citation_txt |
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy / D.M. Schmidtt // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT schmidttdm supersymmetryofaffinetodamodelsasfermionicsymmetryflowsoftheextendedmkdvhierarchy |
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2025-07-10T23:30:12Z |
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2025-07-10T23:30:12Z |
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1837304604903079936 |