--- title: "From worldline to quantum superconformal mechanics with/without oscillatorial terms: D(2,1;α) and sl(2|1) models • 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/6ad2a767639f62b11adbcf0e" 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_~RnJvbSB3b3JsZGxpbmUgdG8gcXVhbnR1bSBzdXBlcmNvbmZvcm1hbCBtZWNoYW5pY3Mgd2l0aC93aXRob3V0IG9zY2lsbGF0b3JpYWwgdGVybXM6IEQoMiwxO86xKSBhbmQgc2woMnwxKSBtb2RlbHM%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~SS5FLiBDdW5oYTsgTi5MLiBIb2xhbmRhOyBGLiBUb3BwYW4%2Cdetalhe_~MjAvMDIvMjAxNw%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmMGUi%2Cs_ZII27Z3m5ZEkJPq5.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "From worldline to quantum superconformal mechanics with/without oscillatorial terms: D(2,1;α) and sl(2|1) models • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~RnJvbSB3b3JsZGxpbmUgdG8gcXVhbnR1bSBzdXBlcmNvbmZvcm1hbCBtZWNoYW5pY3Mgd2l0aC93aXRob3V0IG9zY2lsbGF0b3JpYWwgdGVybXM6IEQoMiwxO86xKSBhbmQgc2woMnwxKSBtb2RlbHM%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~SS5FLiBDdW5oYTsgTi5MLiBIb2xhbmRhOyBGLiBUb3BwYW4%2Cdetalhe_~MjAvMDIvMjAxNw%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmMGUi%2Cs_ZII27Z3m5ZEkJPq5.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **From worldline to quantum superconformal mechanics with/without oscillatorial terms: **D(2,1;α)D(2,1;\\alpha)D(2,1;α)** and **sl(2∣1)sl(2|1)sl(2∣1)** models** **I.E. Cunha; N.L. Holanda; F. Toppan** 02/20/2017 [**Download PDF **0.6 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbcf0e/pdf) [**Contact owner**]() ## **Publication details**
Authors
I.E. Cunha; N.L. Holanda; F. Toppan
Type
Physics Note
Status
Published
Publication date
20/02/2017
Description
In this paper we quantize superconformal $\sigma$-models defined by worldline supermultiplets. \par Two types of superconformal mechanics, with and without a DFF term, are considered. \par Without a DFF term (Calogero potential only) the supersymmetry is unbroken. \par The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory.\par Besides the $osp(1|2)$ examples, we explicitly quantize the superconformally-invariant worldine $\sigma$-models defined by the ${\cal N}=4$ $(1,4,3)$ supermultiplet (with $D(2,1;\alpha)$ invariance, for $\alpha\neq 0,1$) and by the ${\cal N}=2$ $(2,2,0)$ supermultiplet (with two-dimensional target and $sl(2|1)$ invariance). The parameter $\alpha$ is the scaling dimension of the $(1,4,3)$ supermultiplet and, in the DFF case, has a direct interpretation as a vacuum energy. In the DFF case, for the $sl(2|1)$ models, the scaling dimension $\lambda$ is quantized (either $\lambda=\frac{1}{2}+{\mathbb Z}$ or $\lambda={\mathbb Z}$). The ordinary two-dimensional oscillator is recovered from $\lambda=-\frac{1}{2}$. The spectrum of the theory is decomposed into an infinite set of lowest weight representations of $sl(2|1)$. Surprisingly, extra fermionic raising operators, not belonging to $sl(2|1)$, allow to construct the whole spectrum from a single (for $\lambda=\frac{1}{2}+{\mathbb Z}$) bosonic vacuum.
Year
2016
Number
CBPF-NF-006/16
Linked to a thesis
No
Linked to a grant
No
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