Integrable models associated with Myers–Perry–AdS–dS black hole in diverse dimensions

Myers–Perry–AdS–dS black hole exhibits $SO(2,1)\times U\left(n\right)$ symmetry in the near horizon limit in the special case that all rotation parameters are equal. We consider a massive relativistic particle propagating on such a background and reduce it to superintegrable angular mechanics with $U\left(n\right)$ symmetry. A complete set of functionally independent $u\left(n\right)$ generators realized in the model is given.     

ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap $\Delta$ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate $1/T_1$ of a magnetic probe located at a position $\overrightarrow{R}$ around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any $\Delta >0$, $1/T_1$ goes to a constant for $T?{\Gamma }_{\text{k}}$ (Kondo resonance). $1/T_1$ decreases monotonically to zero only for $\Delta =0$. For the asymmetric case, there is a $\Delta$ under which $1/T_1$ decreases monotonically to zero as $T\to 0$, and above which $1/T_1$ saturates, as occurs in the symmetric case for $\Delta >0$. This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.     

Sp(n)U(1)-connections with parallel totally skew-symmetric torsion

We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is $Sp\left(n\right)U\left(1\right)\subset U\left(2n\right)\times U\left(1\right)$, then the manifold is locally isomorphic to the twistor space of a quaternionic Kähler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.     

Sp(n)U(1)-connections with parallel totally skew-symmetric torsion

We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is $Sp\left(n\right)U\left(1\right)\subset U\left(2n\right)\times U\left(1\right)$, then the manifold is locally isomorphic to the twistor space of a quaternionic Kähler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.     

On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space

We prove that an isometric immersion of a simply connected Riemannian surface $M$ in four-dimensional Minkowski space, with given normal bundle $E$ and given mean curvature vector $\overrightarrow{H}\in \Gamma \left(E\right)$, is equivalent to a normalized spinor field $\phi \in \Gamma (\Sigma E\otimes \Sigma M)$ solution of a Dirac equation $D\phi =\overrightarrow{H}\cdot \phi$ on the surface. Using the immersion of the Minkowski space into the complex quaternions, we also obtain a representation of the immersion in terms of the spinor field. We then use these results to describe the flat spacelike surfaces with flat normal bundle and regular Gauss map in four-dimensional Minkowski space, and also the flat surfaces in three-dimensional hyperbolic space, giving spinorial proofs of results by J.A. Gálvez, A. Martínez and F. Milán.