--- title: "Four types of (super)conformal mechanics:D-module reps and invariant actions • 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/6ad2a767639f62b11adbc1b3" 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_~Rm91ciB0eXBlcyBvZiAoc3VwZXIpY29uZm9ybWFsIG1lY2hhbmljczpELW1vZHVsZSByZXBzIGFuZCBpbnZhcmlhbnQgYWN0aW9ucw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_N.L.%2BHolanda%2Cdetalhe_~MTgvMDMvMjAxNA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmMxYjMi%2Cs_xW1Iw9Kyj66KEqL5.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Four types of (super)conformal mechanics:D-module reps and invariant actions • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~Rm91ciB0eXBlcyBvZiAoc3VwZXIpY29uZm9ybWFsIG1lY2hhbmljczpELW1vZHVsZSByZXBzIGFuZCBpbnZhcmlhbnQgYWN0aW9ucw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_N.L.%2BHolanda%2Cdetalhe_~MTgvMDMvMjAxNA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmMxYjMi%2Cs_xW1Iw9Kyj66KEqL5.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Four types of (super)conformal mechanics:D-module reps and invariant actions** **N.L. Holanda** 03/18/2014 [**Download PDF **0.3 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbc1b3/pdf) [**Contact owner**]() ## **Publication details**
Authors
N.L. Holanda
Type
Physics Note
Status
Published
Publication date
18/03/2014
Description
(Super)conformal mechanics in one dimension is induced by parabolic or hyperbolic/trigonometric transformations, either homogeneous (for a scaling dimension $\lambda$) or inhomogeneous (at $\lambda=0$, with $\rho$ an inhomogeneity parameter). Four types of inequivalent (super)conformal actions are thus obtained. With the exclusion of the homogeneous parabolic case, dimensional constants are present. \par Both the inhomogeneity and the insertion of $\lambda$ generalize the construction of Papadopoulos [CQG 30 (2013) 075018; arXiv:1210.1719].\par Inhomogeneous $D$-module reps are presented for the $d=1$ superconformal algebras $osp(1|2)$, $sl(2|1)$, $B(1,1)$ and $A(1,1)$. For centerless superVirasoro algebras $D$-module reps are presented (in the homogeneous case for ${\cal N}=1,2,3,4$; in the inhomogeneous case for ${\cal N}=1,2,3$).\par The four types of $d=1$ superconformal actions are derived for ${\cal N}=1,2,4$ systems. When ${\cal N}=4$, the homogeneously-induced actions are $D(2,1;\alpha)$-invariant ($\alpha$ is critically linked to $\lambda$); the inhomogeneously-induced actions are $A(1,1)$-invariant.\par In $d=2$, for a single bosonic field, the homogeneous transformations induce a conformally invariant power-law action, while the inhomogeneous transformations induce the conformally invariant Liouville action.
Year
2014
Number
CBPF-NF-001/14
Linked to a thesis
Doctorate
Linked to a grant
No
```json {"@context":"https://schema.org","@graph":[{"@id":"https://index.cbpf.br/en#website","@type":"WebSite","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","inLanguage":"en-US","name":"CBPF Index","url":"https://index.cbpf.br/en","publisher":{"@id":"https://index.cbpf.br/#identity"},"translationOfWork":{"@id":"https://index.cbpf.br/#website"}},{"@id":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbc1b3#webpage","@type":"WebPage","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.","name":"Four types of (super)conformal mechanics:D-module reps and invariant actions","url":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbc1b3","isPartOf":{"@id":"https://index.cbpf.br/en#website"},"potentialAction":[{"@type":"ReadAction","target":["https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbc1b3"]}],"primaryImageOfPage":{"@id":"https://index.cbpf.br/#logo"}},{"@id":"https://index.cbpf.br/#identity","@type":"Organization","alternateName":"CBPF","description":"Unidade de pesquisa do Ministério da Ciência, Tecnologia e Inovação dedicada à pesquisa básica em Física, suas aplicações e à formação científica.","email":"web@cbpf.br","legalName":"Centro Brasileiro de Pesquisas Físicas/CBPF","name":"Centro Brasileiro de Pesquisas Físicas","taxID":"04.044.443/0001-35","telephone":"+55-21-2141-7100","url":"https://cbpf.br","address":{"@type":"PostalAddress","streetAddress":"Rua Dr. Xavier Sigaud, 150","addressLocality":"Rio de Janeiro","addressRegion":"RJ","postalCode":"22290-180","addressCountry":"BR"},"logo":{"@id":"https://index.cbpf.br/#logo"},"sameAs":["https://twitter.com/cbpf_mcti"]},{"@id":"https://index.cbpf.br/#logo","@type":"ImageObject","caption":"Centro Brasileiro de Pesquisas Físicas","contentUrl":"https://index.cbpf.br/icon-512x512-light.png","inLanguage":"en-US","url":"https://index.cbpf.br/icon-512x512-light.png"}]} ``` ## Sitemap See the full [sitemap](https://index.cbpf.br/sitemap.md) for all pages.