Heisenberg symmetry and hypermultiplet manifolds

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg U (1). We finally discuss the realization of the latter by gauging appropriate Sp(2, 4) generators in N = 2 conformal supergravity.

The discovery of the appearance of vμ − vτ oscillations

Almost 20 years after the first conceptual design of the experiment, five years of running in the Gran Sasso underground laboratory (LNGS), and billions of billions muon-neutrinos sent from CERN along the CNGS beam, in 2015 the OPERA neutrino detector has allowed the long-awaited discovery of the direct transformation (oscillation) of muon-neutrinos into tau-neutrinos. This result unambiguously confirms the interpretation of the so-called atmospheric channel, after the discovery of neutrino oscillations by the Super-Kamiokande Collaboration in 1998.