Higher Spin AdSd+1_{d+1}/CFTd_d at One Loop

Following arXiv:1308.2337, we carry out one loop tests of higher spin AdS$_{d+1}$/CFT$_d$ correspondences for $d\geq 2$. The Vasiliev theories in AdS$_{d+1}$, which contain each integer spin once, are related to the $U(N)$ singlet sector of the $d$-dimensional CFT of $N$ free complex scalar fields; the minimal theories containing each even spin once -- to the $O(N)$ singlet sector of the CFT of $N$ free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one loop vacuum energies in Euclidean AdS$_{d+1}$. In even $d$ we compare the result with the $O(N^0)$ correction to the $a$-coefficient of the Weyl anomaly; in odd $d$ -- with the $O(N^0)$ correction to the free energy $F$ on the $d$-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of $N$ free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in $d$ dimensions. As explained in arXiv:1308.2337, this result may agree with the $O(N)$ singlet sector of the theory of $N$ real scalar fields, provided the coupling constant in the higher spin theory is identified as $G_N\sim 1/(N-1)$. Our calculations in even $d$ are closely related to finding the regularized $a$-anomalies of conformal higher spin theories. In each even $d$ we identify two such theories with vanishing $a$-anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in $d=5$ obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large $N$ theory is dual to the Vasiliev theory in AdS$_6$ where the bulk scalar is quantized with the alternate boundary condition.Comment: 35 pages. v2: minor improvement

Renyi Entropy and Geometry

Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Renyi entropy and calculable contributions to the perimeter law.Comment: 16 pages, 3 figures; v2 refs added, minor improvement

Measuring Anisotropies in the Cosmic Neutrino Background

Neutrino capture on tritium has emerged as a promising method for detecting the cosmic neutrino background (CvB). We show that relic neutrinos are captured most readily when their spin vectors are anti-aligned with the polarization axis of the tritium nuclei and when they approach along the direction of polarization. As a result, CvB observatories may measure anisotropies in the cosmic neutrino velocity and spin distributions by polarizing the tritium targets. A small dipole anisotropy in the CvB is expected due to the peculiar velocity of the lab frame with respect to the cosmic frame and due to late-time gravitational effects. The PTOLEMY experiment, a tritium observatory currently under construction, should observe a nearly isotropic background. This would serve as a strong test of the cosmological origin of a potential signal. The polarized-target measurements may also constrain non-standard neutrino interactions that would induce larger anisotropies and help discriminate between Majorana versus Dirac neutrinos.Comment: 7 pages, 2 figure

Dark-Matter Harmonics Beyond Annual Modulation

The count rate at dark-matter direct-detection experiments should modulate annually due to the motion of the Earth around the Sun. We show that higher-frequency modulations, including daily modulation, are also present and in some cases are nearly as strong as the annual modulation. These higher-order modes are particularly relevant if (i) the dark matter is light, O(10) GeV, (ii) the scattering is inelastic, or (iii) velocity substructure is present; for these cases, the higher-frequency modes are potentially observable at current and ton-scale detectors. We derive simple expressions for the harmonic modes as functions of the astrophysical and geophysical parameters describing the Earth's orbit, using an updated expression for the Earth's velocity that corrects a common error in the literature. For an isotropic halo velocity distribution, certain ratios of the modes are approximately constant as a function of nuclear recoil energy. Anisotropic distributions can also leave observable features in the harmonic spectrum. Consequently, the higher-order harmonic modes are a powerful tool for identifying a potential signal from interactions with the Galactic dark-matter halo.Comment: 40 pages, 10 figures; v2 refs added, minor improvements; v3 refs added, minor improvements, JCAP versio

Distinguishing Dark Matter from Unresolved Point Sources in the Inner Galaxy with Photon Statistics

Data from the Fermi Large Area Telescope suggests that there is an extended excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential astrophysical sources that contribute to this excess is an important step in verifying whether the signal originates from annihilating dark matter. In this paper, we focus on the potential contribution of unresolved point sources, such as millisecond pulsars (MSPs). We propose that the statistics of the photons---in particular, the flux probability density function (PDF) of the photon counts below the point-source detection threshold---can potentially distinguish between the dark-matter and point-source interpretations. We calculate the flux PDF via the method of generating functions for these two models of the excess. Working in the framework of Bayesian model comparison, we then demonstrate that the flux PDF can potentially provide evidence for an unresolved MSP-like point-source population.Comment: 27 pages, 8 figures; v2, reference added and other minor change

Renyi entropy, stationarity, and entanglement of the conformal scalar

We extend previous work on the perturbative expansion of the Renyi entropy, $S_q$, around $q=1$ for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Renyi entropies. On the other hand, the perturbative results agree with known Renyi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Renyi entropy of ${\cal N}=4$ super-Yang-Mills near $q=1$. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.Comment: 37 page