--- title: "D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb9dc" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~RC1tb2R1bGUgUmVwcmVzZW50YXRpb25zIG9mIE49Miw0LDggU3VwZXJjb25mb3JtYWwgQWxnZWJyYXMgYW5kIFRoZWlyIFN1cGVyY29uZm9ybWFsIE1lY2hhbmljcw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Wmhhbm5hIEt1em5ldHNvdmE7IEYuIFRvcHBhbg%2Cdetalhe_~MDcvMTIvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI5ZGMi%2Cs_71xTAUqAoIK0APIW.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~RC1tb2R1bGUgUmVwcmVzZW50YXRpb25zIG9mIE49Miw0LDggU3VwZXJjb25mb3JtYWwgQWxnZWJyYXMgYW5kIFRoZWlyIFN1cGVyY29uZm9ybWFsIE1lY2hhbmljcw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Wmhhbm5hIEt1em5ldHNvdmE7IEYuIFRvcHBhbg%2Cdetalhe_~MDcvMTIvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI5ZGMi%2Cs_71xTAUqAoIK0APIW.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **D-module Representations of **N=2,4,8{\\cal N}=2,4,8N=2,4,8** Superconformal Algebras and Their Superconformal Mechanics** **Zhanna Kuznetsova; F. Toppan** 12/07/2011 [**Download PDF **0.3 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb9dc/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=D-module%20Representations%20of%20N%3D2%2C4%2C8%20Superconformal%20Algebras%20and%20Their%20Superconformal%20Mechanics) ## **Publication details**
Authors
Zhanna Kuznetsova; F. Toppan
Type
Physics Note
Status
Published
Publication date
07/12/2011
Description
The linear (homogeneous and inhomogeneous) $(k, {\cal N}, {\cal N}-k)$ supermultiplets of the ${\cal N}$-extended one-dimensional Supersymmetry Algebra induce $D$-module representations for the ${\cal N}=2,4,8$ superconformal algebras.\par For ${\cal N}=2$, the $D$-module representations of the $A(1,0)$ superalgebra are obtained. \par For ${\cal N}=4$ and scaling dimension $\lambda=0$, the $D$-module representations of the $A(1,1)$ superalgebra are obtained. For $\lambda\neq 0$, the $D$-module representations of the $D(2,1;\alpha)$ superalgebras are obtained, with $\alpha$ determined in terms of the scaling dimension $\lambda$ according to: $\alpha=-2\lambda$ for $k=4$, i.e. the $(4,4)$ supermultiplet, $\alpha=-\lambda$ for $k=3$, i.e. $(3,4,1)$, and $\alpha=\lambda$ for $k=1$, i.e. $(1,4,3)$. For $\lambda\neq 0$ the $(2,4,2)$ supermultiplet induces a $D$-module representation for the centrally extended $sl(2|2)$ superalgebra.\par For ${\cal N}=8$, the $(8,8)$ root supermultiplet induces a $D$-module representation of the $D(4,1)$ superalgebra at the fixed value $\lambda=\frac{1}{4}$.\par A Lagrangian framework to construct one-dimensional, off-shell, superconformal invariant actions from single-particle and multi-particles $D$-module representations is discussed. It is applied to explicitly construct invariant actions for the homogeneous and inhomogeneous ${\cal N}=4$ $(1,4,3)$ $D$-module representations (in the last case for several interacting supermultiplets of different chirality).
Year
2011
Number
CBPF-NF-015/11
Linked to a thesis
No
Linked to a grant
No
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