---
title: "Critical D-module reps for finite 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."
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**Physics Note****Published**

# **Critical **DDD**-module reps for finite superconformal algebras and their superconformal mechanics"**

**F. Toppan**

02/07/2013

[**Download PDF **1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbbc56/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Critical%20D-module%20reps%20for%20finite%20superconformal%20algebras%20and%20their%20superconformal%20mechanics%22)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>F. Toppan</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>07/02/2013</dd>

<dt>Description</dt>
<dd>The simple finite Lie superalgebras $D(2,1;\alpha)$, $G(3)$, $D(4,1)$, $D(2,2)$, $A(3,1)$ and $F(4)$ admit $D$-module representations, given by a set of differential operators of a single variable $t\in \mathbb{R}$, at a critical value of the scaling dimension $\lambda$. These superalgebras are one-dimensional ${\cal N}$-extended superconformal algebras with ${\cal N}=4$ ($D(2,1;\alpha)$), ${\cal N}=7$ ($G(3)$) and ${\cal N}=8$ (the remaining ones). The critical $D$-module reps induce invariant actions in the Lagrangian framework for superconformal mechanics in $D$ target dimensions. The ${\cal N}=8$ critical scalings $\lambda=\frac{1}{D-4}$ are linked to the $D$-dimensional harmonic functions with $D=1,2,3,5,6,7,8$. This talk is based on {J. Math. Phys.} {\bf 53} (2012) 043513 (arXiv:1112.0995), {J. Math. Phys.} {\bf 53} (2012) 103518 (arXiv:1208.3612) and some extra material.</dd>

<dt>Year</dt>
<dd>2012</dd>

<dt>Number</dt>
<dd>CBPF-NF-014/12</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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