Group manifolds and homogeneous spaces with HKT geometry: The role of automorphisms

  title={Group manifolds and homogeneous spaces with HKT geometry: The role of automorphisms},
  author={Andrei V. Smilga},
  journal={Nuclear Physics},
  • A. Smilga
  • Published 15 February 2020
  • Mathematics
  • Nuclear Physics

Figures from this paper


Homogeneous HKT and QKT manifolds
We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, $G/K$, using an invariant metric on $G$ and the canonical connection. For this a decomposition of the Lie
Hyperkaehler manifolds with torsion, supersymmetry and Hodge theory
Let M be a hypercomplex Hermitian manifold, (M,I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction
Geometry of Hyper-Kähler Connections with Torsion
Abstract:The internal space of a N = 4 supersymmetric model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy in SP(n). We study the mathematical background of
Complex Analytic Coordinates in Almost Complex Manifolds
A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic
A note on the Atiyah-Singer index theorem for manifolds with totally antisymmetric H torsion
The author presents two proofs of the Atiyah-Singer index theorem (1969) for the Dirac operator for even-dimensional orientable manifolds without boundary with totally antisymmetric torsion with
Generic HKT geometries in the harmonic superspace approach
We explain how a generic HKT geometry can be derived using the language of N = 4 supersymmetric quantum mechanics. To this end, one should consider a Lagrangian involving several (4,4,0) multiplets
The Geometry of Supersymmetric Quantum Mechanics
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the
New geometry from heterotic supersymmetry
The authors show that the bosonic sector of a (4,0) supersymmetric sigma -model is a quasi Ricci-flat manifold with a closed torsion and vanishing scalar curvature; in the torsionless limit they