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

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

Evidence for Unresolved Gamma-Ray Point Sources in the Inner Galaxy

We present a new method to characterize unresolved point sources (PSs), generalizing traditional template fits to account for non-Poissonian photon statistics. We apply this method to Fermi Large Area Telescope gamma-ray data to characterize PS populations at high latitudes and in the Inner Galaxy. We find that PSs (resolved and unresolved) account for ~50% of the total extragalactic gamma-ray background in the energy range ~1.9 to 11.9 GeV. Within 10$^\circ$ of the Galactic Center with $|b| \geq 2^\circ$, we find that ~5-10% of the flux can be accounted for by a population of unresolved PSs, distributed consistently with the observed ~GeV gamma-ray excess in this region. The excess is fully absorbed by such a population, in preference to dark-matter annihilation. The inferred source population is dominated by near-threshold sources, which may be detectable in future searches.Comment: 7+22 pages, 4+18 figures; v2, minor changes, new Pass 8 data analyzed (conclusions unchanged); v3, PRL version, substantive improvements and additional checks (conclusion unchanged

Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''

In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general dimensionality d). In particular, they explore a presumed connection between non-integrable interactions and Tsallis's non-extensive statistics. We point out that (i) non-integrable interactions provide no more motivation for Tsallis statistics than do integrable interactions, i.e., Gibbs statistics remain meaningful for the non-integrable case, and in fact provide a {\em complete and exact treatment}; and (ii) there are undesirable features of the method ST use to regulate the non-integrable interactions.Comment: Accepted for publication in Phys. Rev. Let

Nephrectomy Delay of More than 10 Weeks from Diagnosis Is Associated with Decreased Overall Survival in pT3 RCC

In this study, we aimed to evaluate the impact of surgical wait time (SWT) on outcomes of patients with renal cell carcinoma (RCC), and to investigate risk factors associated with prolonged SWT. Using the National Cancer Database, we retrospectively reviewed the records of patients with pT3 RCC treated with radical or partial nephrectomy between 2004 and 2014. The cohort was divided based on SWT. The primary outcome was 5-year overall survival (OS). Logistic regression analysis was used to investigate the risk factors associated with delayed surgery. Cox proportional hazards models were fitted to assess relations between SWT and 5-year OS after adjusting for confounding factors. A total of 22,653 patients were included in the analysis. Patients with SWT &gt; 10 weeks had higher occurrence of upstaging. Using logistic regression, we found that female patients, African-American or Spanish origin patients, treatment in academic or integrated network cancer center, lack of insurance, median household income of &lt;$38,000, and the Charlson–Deyo score of ≥1 were more likely to have prolonged SWT. SWT &gt; 10 weeks was associated with decreased 5-year OS (hazard ratio [HR], 1.24; 95% confidence interval [CI], 1.15–1.33). This risk was not markedly attenuated after adjusting for confounding variables, including age, gender, race, insurance status, Charlson–Deyo score, tumor size, and surgical margin status (adjusted HR, 1.13; 95% CI, 1.04–1.24). In conclusion, the vast majority of patients underwent surgery within 10 weeks. There is a statistically significant trend of increasing SWT over the study period. SWT &gt; 10 weeks is associated with decreased 5-year OS