Critical scaling dimension of D-module representations of N=4,7,8 superconformal algebras and constraints on superconformal mechanics
- CBPF, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180, Rio de Janeiro (RJ) (Brazil)
At critical values of the scaling dimension {lambda}, supermultiplets of the global 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 N=4,8 and global supermultiplets (k,N,N-k), the exceptional superalgebras D(2, 1;{alpha}) are recovered for N=4, with a relation between {alpha} and the scaling dimension given by {alpha}= (2 -k){lambda}. For N=8 and k{ne} 4 all four N=8 finite superconformal algebras are recovered, at the critical values {lambda}{sub k}=(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 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{sub 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 N=4 superconformal mechanics. The existence of new superconformal models is pointed out. For example, coupled (1, 4, 3) and (3, 4, 1) supermultiplets generate an N=4 superconformal mechanics if {lambda} is related to the golden ratio. The relation between classical versus quantum D-module representations is presented.
- OSTI ID:
- 22093765
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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