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The Geometry of (Super) Conformal Quantum Mechanics
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The Geometry of (Super) Conformal Quantum Mechanics
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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.
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Cited by 1 Pith paper
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On conformal symmetry in large-$N$ quiver mechanics
At large rank N, the fixed-point formula for the quiver superconformal index equals the Ω_uneq contribution to the microscopic scaling BPS index of Beaujard–Mondal–Pioline, a piece previously invisible on the Coulomb branch.
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