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- W1993821071 abstract "At critical values of the scaling dimension $lambda$, supermultiplets of the global ${cal N}$-Extended one-dimensional Supersymmetry algebra induce $D$-module representations of finite superconformal algebras (the latters being identified in terms of the global supermultiplet and its critical scaling dimension). For ${cal N}=4,8$ and global supermultiplets $(k, {cal N}, {cal N}-k)$, the exceptional superalgebras $D(2,1;alpha)$ are recovered for ${cal N}=4$, with a relation between $alpha$ and the scaling dimension given by $alpha= (2-k)lambda$. For ${cal N}=8$ and $kneq 4$ all four ${cal N}=8$ finite superconformal algebras are recovered, at the critical values $lambda_k = frac{1}{k-4}$, with the following identifications: D(4,1) for $k=0,8$, F(4) for $k=1,7$, A(3,1) for $k=2,6$ and D(2,2) for $k=3,5$. The ${cal N}=7$ global supermultiplet $(1,7,7,1)$ induces, at $lambda= -1/4$, a $D$-module representation of the exceptional superalgebra G(3). $D$-module representations are applicable to the construction of superconformal mechanics in a Lagrangian setting. The isomorphism of the $D(2,1;alpha)$ algebras under an $S_3$ group action on $alpha$, coupled with the relation between $alpha$ and the scaling dimension $lambda$, induces non-trivial constraints on the admissible models of ${cal N}=4$ superconformal mechanics. The existence of new superconformal models is pointed out. E.g., coupled $(1,4,3)$ and $(3,4,1)$ supermultiplets generate an ${cal N}=4$ superconformal mechanics if $lambda$ is related to the golden ratio. The relation between classical versus quantum $D$-module representations is presented." @default.
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- W1993821071 date "2012-10-01" @default.
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- W1993821071 title "Critical scaling dimension of <i>D</i>-module representations of N=4,7,8 superconformal algebras and constraints on superconformal mechanics" @default.
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- W1993821071 doi "https://doi.org/10.1063/1.4758923" @default.
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