Superconformal SU(1,1|n) mechanics

Abstract

Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1,1|2) in mechanics. Remarking that SU(1,1|2) is a particular member of a chain of supergroups SU(1,1|n) parametrized by an integer n, here we begin a systematic study of SU(1,1|n) multi-particle mechanics. A representation of the superconformal algebra su(1,1|n) is constructed on the phase space spanned by m copies of the (1,2n,2n-1) supermultiplet. We show that the dynamics is governed by two prepotentials V and F, and the Witten-Dijkgraaf-Verlinde-Verlinde equation for F shows up as a consequence of a more general fourth-order equation. All solutions to the latter in terms of root systems reveal decoupled models only. An extension of the dynamical content of the (1,2n,2n-1) supermultiplet by angular variables in a way similar to the SU(1,1|2) case is problematic.

1+8 pages; v2: eq.(14) corrected, one ref. added, published version

References in corpus (7)

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• WDVV equations and invariant bi-Hamiltonian formalism
• Super 0--brane action on the coset space of $D(2,1;\alpha )$ supergroup
• Superfield approach to higher derivative N=1 superconformal mechanics
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• On $OSp(N|2)$ superconformal mechanics