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 aδ a whose associated one-form D a dX 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 bδ b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given.
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Received: 3 September 1999 / Accepted: 30 January 2000
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Michelson, J., Strominger, A. The Geometry of¶(Super) Conformal Quantum Mechanics. Commun. Math. Phys. 213, 1–17 (2000). https://doi.org/10.1007/PL00005528
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DOI: https://doi.org/10.1007/PL00005528