Superconformal Calogero models as a gauged matrix mechanics

Source: arXiv

ABSTRACT We present basics of the gauged superfield approach to constructing
N-superconformal multi-particle Calogero-type systems developed in
arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is
illustrated by the multi-particle systems possessing SU(1,1|1) and
D(2,1;\alpha) supersymmetries, as well as by the model of new N=4
superconformal quantum mechanics.

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    ABSTRACT: Some aspects of harmonic superspace are discussed.
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    ABSTRACT: N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,R) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector $D^a$ whose associated one-form $D_a$ is closed. Further, the SL(2,R) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry $D^a I_a{^b} \partial_b$. Conditions for extension to the superconformal group D(2,1;\alpha), which involve a triplet of complex structures and SU(2) x SU(2) isometries, are derived. Examples are given. Comment: 23 pages harvmac. Conventions simplified; typos corrected; references added
    Communications in Mathematical Physics 07/1999; · 1.97 Impact Factor
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    ABSTRACT: A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the one-particle case of the new N=4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th]. Classical and quantum generators of the osp(4|2) superalgebra are constructed on physical states. As opposed to other realizations of N=4 superconformal algebras, all supertranslation generators are linear in the odd variables, similarly to the N=2 case. The bosonic sector of the component action is standard one-particle (dilatonic) conformal mechanics accompanied by an SU(2)/U(1) Wess-Zumino term, which gives rise to a fuzzy sphere upon quantization. The strength of the conformal potential is quantized. Comment: 1+20 pages, v2: typos fixed, for publication in JHEP
    Journal of High Energy Physics 05/2009; · 5.62 Impact Factor


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