arXiv subjects
Publications and source records attributed to Pierre-Yves Casteill.
In order to establish an explicit connection between four-dimensional Hall effect on $S^4$ and six-dimensional Hall effect on $\DC P^3$, we perform the Hamiltonian reduction of a particle moving on $\DC P^3$ in a constant magnetic field to the four-dimensional Hall mechanics (i.e. a particle on $S^4$ in a SU(2) instanton field). This reduction corresponds to fixing the isospin of the latter system.
The quantum equivalence between sigma-models and their non-abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group SU(2) times U(1). We prove that the one-loop renormalisability of the initial torsionless sigma-models is equivalent to the one-loop renormalisability of the T-dualised torsionful model. For a subclass of Kahler original metrics, the dual partners are still Kahler (with torsion).
We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses $U(1)\times U(1)$ isometry, contains as special cases the quaternionic-Kähler extensions of the Taub-NUT and Eguchi-Hanson metrics and exhibits an extra one-parameter freedom which disappears in the hyper-Kähler limit. Some emphasis is put on the relation between this class of quaternionic-Kähler metrics and self-dual Weyl solutions of the coupled Einstein-Maxwell equations. The relation between our explicit results and the recent general ansatz of Calderbank and Pedersen for quaternionic-Kähler metrics with $U(1)\times U(1)$ isometries is traced in detail.
Starting from the generic harmonic superspace action of the quaternion-Kähler sigma models and using the quotient approach we present, in an explicit form, a quaternion-Kähler extension of the double Taub-NUT metric. It possesses $U(1)\times U(1)$ isometry and supplies a new example of non-homogeneous Einstein metric with self-dual Weyl tensor.