Comments on HKT supersymmetric sigma models and their Hamiltonian reduction. (English) Zbl 1316.81069
Summary: Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT (‘hyper-Kähler with torsion’) supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric ‘hypercomplex structure’ tensor \(\mathcal{I}_{jk}\) which plays the same role for the HKT models as the complex structure tensor for the Kähler models. When the Hamiltonian and supercharges commute with the momenta conjugate to the imaginary parts of the complex coordinates, one can perform a Hamiltonian reduction. The models thus obtained represent a special class of quasicomplex sigma models introduced recently by E. A. Ivanov and A. V. Smilga [SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 069, 17 p. (2013; Zbl 1287.81108)].
MSC:
81T10 | Model quantum field theories |
81Q60 | Supersymmetry and quantum mechanics |
81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
70S20 | More general nonquantum field theories in mechanics of particles and systems |
81T60 | Supersymmetric field theories in quantum mechanics |
53C26 | Hyper-Kähler and quaternionic Kähler geometry, “special” geometry |