Constraining conformal field theories with a slightly broken higher spin symmetry

We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Persistent deNOx Ability of CaAl2O4:(Eu, Nd)/TiO2-xNy Luminescent Photocatalyst

The properties of the dusty tori in active galactic nuclei (AGNs) have been investigated in detail, mainly focusing on the geometry and components; however, the kinematics of the torus is still not clear. The narrow iron K$\alpha$ line at 6.4 keV is thought to be produced by the X-ray reflection from the torus. Thus, the velocity-resolved reverberation mapping of it is able to constrain the kinematics of the torus. Such effort is limited by the spectral resolution of current CCD detectors and should be possible with the microcalorimeter on the next generation X-ray satellite. In this paper, we first construct the response functions of the torus under a uniform inflow, a Keplerian rotation, and a uniform outflow. Then the energy-dependent light curve of the narrow iron K$\alpha$ line is simulated according to the performance of the X-ray Integral Field Unit in Athena. Finally, the energy-dependent cross-correlation function is calculated to reveal the kinematic signal. According to our results, one hundred observations with 5 ks exposure of each are sufficient to distinguish the above three velocity fields. Although the real geometry and velocity field of the torus could be more complex than we assumed, the present result proves the feasibility of the velocity-resolved reverberation mapping of the narrow iron K$\alpha$ line. The combination of the dynamics of the torus with those of the broad line region and the host galaxy is instructive for the understanding of the feeding and feedback process of AGNs.Comment: 6 pages, 5 figures, ApJ Letters accepte

Holography, Unfolding and Higher-Spin Theory

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos correcte

The Higher Spin/Vector Model Duality

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev. v2: references adde

Minimal Model Holography

We review the duality relating 2d W_N minimal model CFTs, in a large N 't Hooft like limit, to higher spin gravitational theories on AdS_3.Comment: 54 pages, 1 figure; Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev. v2. minor change

Parental social contact in the work place and the risk of childhood acute lymphoblastic leukaemia

To study the possible relation between parental social contact through occupation, a marker for a child's risk of infection, and childhood acute lymphoblastic leukaemia (ALL), the parents of 294 children with ALL aged 0–14.9 years and 376 matched controls were interviewed about their jobs after their child's birth up to the age of 3 years. Job titles were assigned to a level of social contact, and an index of occupational social contact months was created using the level and the job duration. Positive interactions between this index and rural residence associated with an increased risk of childhood ALL and common ALL (c-ALL) were observed (interaction P-value=0.02 for both, using tertiles of contact months; interaction P-value=0.05 and 0.02 for ALL and c-ALL, respectively, using continuous contact months); such findings were not observed when job durations were ignored. Our data suggest that duration of parental occupation may be important when examining the association between parental social contact in the workplace and childhood leukaemia