New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models
A novel feature of the Z2×Z2-graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the “ex...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-06-01
|
| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323001311 |
| _version_ | 1797823764053884928 |
|---|---|
| author | Naruhiko Aizawa Ren Ito Zhanna Kuznetsova Francesco Toppan |
| author_facet | Naruhiko Aizawa Ren Ito Zhanna Kuznetsova Francesco Toppan |
| author_sort | Naruhiko Aizawa |
| collection | DOAJ |
| description | A novel feature of the Z2×Z2-graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the “exotic bosonic coordinate” was not considered by previous works on the one-dimensional Z2×Z2-graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained.The graded superspace calculus of the Z2×Z2-graded worldline super-Poincaré algebra induces two-dimensional Z2×Z2-graded relativistic models; they are invariant under a new Z2×Z2-graded 2D super-Poincaré algebra which differs from the previous two Z2×Z2-graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S1, a Z2×Z2-graded closed string with periodic boundary conditions is derived.The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger (β-deformed, where β≥0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β=0) is obtained. While the spectrum of the β=0 point-particle models is degenerate (due to its relation with an N=2 supersymmetry), this is no longer the case for the β>0 models. |
| first_indexed | 2024-03-13T10:28:46Z |
| format | Article |
| id | doaj.art-50c1e8d99a6341b9917793b336f27aa3 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-03-13T10:28:46Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-50c1e8d99a6341b9917793b336f27aa32023-05-19T04:44:54ZengElsevierNuclear Physics B0550-32132023-06-01991116202New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic modelsNaruhiko Aizawa0Ren Ito1Zhanna Kuznetsova2Francesco Toppan3Department of Physics, Graduate School of Science, Osaka Metropolitan University, Nakamozu Campus, Sakai, Osaka 599-8531, JapanDepartment of Physics, Graduate School of Science, Osaka Metropolitan University, Nakamozu Campus, Sakai, Osaka 599-8531, JapanUFABC, Av. dos Estados 5001, Bangu, cep 09210-580, Santo André, SP, BrazilCBPF, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180, Rio de Janeiro, RJ, Brazil; Corresponding author.A novel feature of the Z2×Z2-graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the “exotic bosonic coordinate” was not considered by previous works on the one-dimensional Z2×Z2-graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained.The graded superspace calculus of the Z2×Z2-graded worldline super-Poincaré algebra induces two-dimensional Z2×Z2-graded relativistic models; they are invariant under a new Z2×Z2-graded 2D super-Poincaré algebra which differs from the previous two Z2×Z2-graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S1, a Z2×Z2-graded closed string with periodic boundary conditions is derived.The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger (β-deformed, where β≥0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β=0) is obtained. While the spectrum of the β=0 point-particle models is degenerate (due to its relation with an N=2 supersymmetry), this is no longer the case for the β>0 models.http://www.sciencedirect.com/science/article/pii/S0550321323001311 |
| spellingShingle | Naruhiko Aizawa Ren Ito Zhanna Kuznetsova Francesco Toppan New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models Nuclear Physics B |
| title | New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models |
| title_full | New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models |
| title_fullStr | New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models |
| title_full_unstemmed | New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models |
| title_short | New aspects of the Z2×Z2-graded 1D superspace: Induced strings and 2D relativistic models |
| title_sort | new aspects of the z2 z2 graded 1d superspace induced strings and 2d relativistic models |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323001311 |
| work_keys_str_mv | AT naruhikoaizawa newaspectsofthez2z2graded1dsuperspaceinducedstringsand2drelativisticmodels AT renito newaspectsofthez2z2graded1dsuperspaceinducedstringsand2drelativisticmodels AT zhannakuznetsova newaspectsofthez2z2graded1dsuperspaceinducedstringsand2drelativisticmodels AT francescotoppan newaspectsofthez2z2graded1dsuperspaceinducedstringsand2drelativisticmodels |