Acting as powerful gravitational lenses, the strong lensing galaxy clusters of the deep Hubble Frontier Fields (HFF) program permit access to lower-luminosity galaxies lying at higher redshifts than hitherto possible. We analyzed the HFF to measure the volume density of Lyman-break galaxies at z > 4.75 by identifying a complete and reliable sample up to z 10. A marked deficit of such galaxies was uncovered in the highly magnified regions of the clusters relative to their outskirts, implying that the magnification of the sky area dominates over additional faint galaxies magnified above the flux limit. This negative magnification bias is consistent with a slow rollover at the faint end of the UV luminosity function, and indicates a preference for Bose-Einstein condensate dark matter with a light boson mass of m B 10 −22 eV over standard cold dark matter. We emphasize that measuring the magnification bias requires no correction for multiply lensed images (with typically three or more images per source), whereas directly reconstructing the luminosity function will lead to an overestimate unless such images can be exhaustively matched up, especially at the faint end that is accessible only in the strongly lensed regions. In addition, we detected a distinctive downward transition in galaxy number density at z 8, which may be linked to the relatively late reionization reported by Planck. Our results suggests that JWST will likely peer into an "abyss" with essentially no galaxies detected in deep NIR imaging at z > 10.

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We analyze the global symmetries and anomalies of 4d $$ \mathcal{N} $$ N = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved ℂ2/ℤk singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G4-flux configuration labeled by a collection of 2(k − 1) flux quanta, {Ni}. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the ’t Hooft anomalies for continuous symmetries at leading order in the limit of large N, Ni.

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2/ℤk singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2/ℤk singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.