We present ultraviolet, optical, and infrared photometry of the afterglow of the X-ray flash XRF 050416A taken between approximately 100 seconds and 36 days after the burst. We find an intrinsic spectral slope between 1930 and 22,200 Angstrom of beta = -1.14 +/- 0.20 and a decay rate of alpha = -0.86 +/- 0.15. There is no evidence for a change in the decay rate between approximately 0.7 and 4.7 days after the burst. Our data implies that there is no spectral break between the optical and X-ray bands between 0.7 and 4.7 days after the burst, and is consistent with the cooling break being redward of the K_s band (22,200 Angstrom) at 0.7 days. The combined ultraviolet/optical/infrared spectral energy distribution shows no evidence for a significant amount of extinction in the host galaxy along the line of sight to XRF 050416A. Our data suggest that the extragalactic extinction along the line of sight to the burst is only approximately A_V = 0.2 mag, which is significantly less than the extinction expected from the hydrogen column density inferred from $X$-ray observations of XRF 050416A assuming a dust-to-gas ratio similar to what is found for the Milky Way. The observed extinction, however, is consistent with the dust-to-gas ratio seen in the Small Magellanic Cloud. We suggest that XRF 050416A may have a two-component jet similar to what has been proposed for GRB 030329. If this is the case the lack of an observed jet break between 0.7 and 42 days is an illusion due to emission from the wide jet dominating the afterglow after approximately 1.5 days.

This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked out in the first paper of the series, 1101.1126 [hep-th], a thorough analysis of rigid symmetries of the sigma model is carried out with emphasis on algebraic structures on generalised tangent bundles over the target space of the theory and over its state space that give rise to a realisation of the symmetry algebra on states. The analysis leads to a proposal for a novel differential-algebraic construct extending the original definition of the (gerbe-twisted) Courant algebroid on the generalised tangent bundles over the target space in a manner codetermined by the structure of the 2-category of abelian bundle gerbes with connection over it. The construct admits a neat interpretation in terms of a relative Cartan calculus associated with the hierarchy of manifolds that compose the target space of the multiphase sigma model. The paper also discusses at length the gauge anomaly for the rigid symmetries, derived and quantified cohomologically in a previous work of Gawȩdzki, Waldorf and the author. The ensuing reinterpretation of the small gauge anomaly in terms of the twisted rel. Courant algebroid modelling the Poisson algebra of Noether charges of the symmetries is elucidated through an equivalence between a category built from data of the gauged sigma model and that of principal bundles over the worldsheet with a structural action groupoid based on the target space. Finally, the large gauge anomaly is identified with the obstruction to the existence of topological defect networks implementing the action of the gauge group of the gauged sigma model and those giving a local trivialisation of a gauge bundle of an arbitrary topology over the worldsheet.