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.

Enhanced depth imaging optical coherence tomography of congenital cavitary optic disc anomaly (CODA).

AIM To report the finding of extension of the 4th hyper-reflective band and retinal tissue into the optic disc in patients with cavitary optic disc anomalies (CODAs). METHODS In this observational study, 10 patients (18 eyes) with sporadic or autosomal dominant CODA were evaluated with enhanced depth imaging optical coherence tomography (EDI-OCT) and colour fundus images for the presence of 4th hyper-reflective band extension into the optic disc. RESULTS Of 10 CODA patients (18 eyes), five patients (8 eyes) showed a definite 4th hyper-reflective band (presumed retinal pigment epithelium (RPE)) extension into the optic disc. In these five patients (seven eyes), the inner retinal layers also extended with the 4th hyper-reflective band into the optic disc. Best corrected visual acuity ranged from 20/20 to 20/200. In three patients (four eyes), retinal splitting/schisis was present and in two patients (two eyes), the macula was involved. In all cases, the 4th hyper-reflective band extended far beyond the termination of the choroid into the optic disc. The RPE extension was found either temporally or nasally in areas of optic nerve head excavation, most often adjacent to peripapillary pigment. Compared with eyes without RPE extension, eyes with RPE extension were more myopic (mean dioptres -0.9±2.6 vs -8.8±5, p=0.043). CONCLUSIONS The RPE usually stops near the optic nerve border separated by a border tissue. With CODA, extension of this hyper-reflective band and retinal tissue into the disc is possible and best evaluable using EDI-OCT or analogous image modalities. Whether this is a finding specific for CODA, linked to specific gene loci or is also seen in patients with other optic disc abnormalities needs further evaluation.