Finite higher spin transformations from exponentiation

We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of ${\rm hs}(\lambda)$ in a dense set are exponentiable, when pictured in certain representations of ${\rm hs}(\lambda)$, induced from representations of $SL(2,\mathbb{R})$ in the complementary series. We also provide a geometric picture of higher spin gauge transformations clarifying the physical origin of these representations. This allows us to construct an infinite-dimensional topological group $HS(\lambda)$ of finite higher spin symmetries. Interestingly, this construction is possible only for $0 \leq \lambda \leq 1$, which are the values for which the higher spin theory is believed to be unitary and for which the Gaberdiel-Gopakumar duality holds. We exponentiate explicitly various commutative subalgebras of ${\rm hs}(\lambda)$. Among those, we identify families of elements of ${\rm hs}(\lambda)$ exponentiating to the unit of $HS(\lambda)$, generalizing the logarithms of the holonomies of BTZ black hole connections. Our techniques are generalizable to the Lie algebras relevant to higher spin theories in dimensions above three.Comment: 34 pages. v3: references added. Added a discussion of the Euclidean higher spin symmetry group. Unlike what was claimed in a previous version, the formalism developed here can be applied to the Euclidean case as wel

Mid-infrared size survey of Young Stellar Objects: Description of Keck segment-tilting experiment and basic results

The mid-infrared properties of pre-planetary disks are sensitive to the temperature and flaring profiles of disks for the regions where planet formation is expected to occur. In order to constrain theories of planet formation, we have carried out a mid-infrared (wavelength 10.7 microns) size survey of young stellar objects using the segmented Keck telescope in a novel configuration. We introduced a customized pattern of tilts to individual mirror segments to allow efficient sparse-aperture interferometry, allowing full aperture synthesis imaging with higher calibration precision than traditional imaging. In contrast to previous surveys on smaller telescopes and with poorer calibration precision, we find most objects in our sample are partially resolved. Here we present the main observational results of our survey of 5 embedded massive protostars, 25 Herbig Ae/Be stars, 3 T Tauri stars, 1 FU Ori system, and 5 emission-line objects of uncertain classification. The observed mid-infrared sizes do not obey the size-luminosity relation found at near-infrared wavelengths and a companion paper will provide further modelling analysis of this sample. In addition, we report imaging results for a few of the most resolved objects, including complex emission around embedded massive protostars, the photoevaporating circumbinary disk around MWC 361A, and the subarcsecond binaries T Tau, FU Ori and MWC 1080.Comment: Accepted by Astrophysical Journal. 38 pages. 9 figure