Physics NotePublished
D-module Representations of Superconformal Algebras and Their Superconformal Mechanics
Zhanna Kuznetsova; F. Toppan
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