N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets

N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators in the superalgebra form analogues of the irreducible (1,4,3)-, (2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a turns out to be constrained by the Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2,1;a), a remains arbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work.Comment: V2: 9 pages. Introductory part extended, two references added. The version to appear in JHE

SU(1,2) invariance in two-dimensional oscillator

Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.Comment: 7 page

NuSTAR and XMM-Newton observations of the ultraluminous X-ray source NGC 5643 X-1

We present a high-quality hard X-ray spectrum of the ultraluminous X-ray source (ULX) NGC 5643 X-1 measured with NuSTAR in May-June 2014. We have obtained this spectrum by carefully separating the signals from the ULX and from the active nucleus of its host galaxy NGC 5643 located 0.8 arcmin away. Together with long XMM-Newton observations performed in July 2009 and August 2014, the NuSTAR data confidently reveal a high-energy cutoff in the spectrum of NGC 5643 X-1 above ~10 keV, which is a characteristic signature of ULXs. The NuSTAR and XMM-Newton data are consistent with the source having a constant luminosity ~1.5E40 erg/s (0.2-12 keV) in all but the latest observation (August 2014) when it brightened to ~3E40 erg/s. This increase is associated with the dominant, hard spectral component (presumably collimated emission from the inner regions of a supercritical accretion disc), while an additional, soft component (with a temperature ~0.3 keV if described by multicolor disk emission), possibly associated with a massive wind outflowing from the disk, is also evident in the spectrum but does not exhibit significant variability.Comment: 8 pages, 3 figures, 4 tables, Accepted for publication in MNRA