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Chapter: On harmonic superspace
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ABSTRACT: Some aspects of harmonic superspace are discussed.05/2007: pages 6878;  [Show abstract] [Hide abstract]
ABSTRACT: Nparticle quantum mechanics described by a sigma model with an Ndimensional 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 oneform $D_a$ is closed. Further, the SL(2,R) can always be extended to Osp(12) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,11) 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 addedCommunications in Mathematical Physics 07/1999; · 1.97 Impact Factor 
Article: OSp(42) Superconformal Mechanics
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ABSTRACT: A new superconformal mechanics with OSp(42) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the oneparticle case of the new N=4 super Calogero model recently proposed in arXiv:0812.4276 [hepth]. Classical and quantum generators of the osp(42) 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 oneparticle (dilatonic) conformal mechanics accompanied by an SU(2)/U(1) WessZumino 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 JHEPJournal of High Energy Physics 05/2009; · 5.62 Impact Factor
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