Numerical determination of entanglement entropy for a sphere

We apply Srednicki's regularization to extract the logarithmic term in the entanglement entropy produced by tracing out a real, massless, scalar field inside a three dimensional sphere in 3+1 flat spacetime. We find numerically that the coefficient of the logarithm is -1/90 to 0.2 percent accuracy, in agreement with an existing analytical result

General solutions of the Wess-Zumino consistency condition for the Weyl anomalies

The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.Comment: 9 pages. RevTeX fil

Violation of Energy Bounds in Designer Gravity

We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W. It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W, if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos corrected, reference adde

A classification of local Weyl invariants in D=8

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde

N=2 Superconformal boundary states for free bosons and fermions

The most general N=2 superconformal boundary states for the c=3 theory consisting of two (uncompactified) free bosons and fermions are constructed. It is shown that the only N=2 boundary states are the familiar Dirichlet boundary states, as well as the Neumann boundary states with an arbitrary electric field.Comment: 20 pages, latex, references added, discussion of GSO projection clarifie

The giant Cretaceous coelacanth (Actinistia, Sarcopterygii) Megalocoelacanthus dobiei Schwimmer, Stewart & Williams, 1994, and its bearing on Latimerioidei interrelationships

We present a redescription of Megalocoelacanthus dobiei, a giant fossil coelacanth from Upper Cretaceous strata of North America. Megalocoelacanthus has been previously described on the basis of composite material that consisted of isolated elements. Consequently, many aspects of its anatomy have remained unknown as well as its phylogenetic relationships with other coelacanths. Previous studies have suggested that Megalocoelacanthus is closer to Latimeria and Macropoma than to Mawsonia. However, this assumption was based only on the overall similarity of few anatomical features, rather than on a phylogenetic character analysis. A new, and outstandingly preserved specimen from the Niobrara Formation in Kansas allows the detailed description of the skull of Megalocoelacanthus and elucidation of its phylogenetic relationships with other coelacanths. Although strongly flattened, the skull and jaws are well preserved and show many derived features that are shared with Latimeriidae such as Latimeria, Macropoma and Libys. Notably, the parietonasal shield is narrow and flanked by very large, continuous vacuities forming the supraorbital sensory line canal. Such an unusual morphology is also known in Libys. Some other features of Megalocoelacanthus, such as its large size and the absence of teeth are shared with the mawsoniid genera Mawsonia and Axelrodichthys. Our cladistic analysis supports the sister-group relationship of Megalocoelacanthus and Libys within Latimeriidae. This topology suggests that toothless, large-sized coelacanths evolved independently in both Latimeriidae and Mawsoniidae during the Mesozoic. Based on previous topologies and on ours, we then review the high-level taxonomy of Latimerioidei and propose new systematic phylogenetic definitions