Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations

Classical conformal blocks naturally appear in the large central charge limit of 2D Virasoro conformal blocks. In the $AdS_{3}/CFT_{2}$ correspondence, they are related to classical bulk actions and are used to calculate entanglement entropy and geodesic lengths. In this work, we discuss the identification of classical conformal blocks and the Painlev\'e VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun's equation from the isomonodromic $\tau$-function. We also discuss how the $c = 1$ expansion of the $\tau$-function leads to a novel approach to calculate the 4-point classical conformal block.Comment: 32+10 pages, 2 figures; v3: upgraded notation, discussion on moduli space and monodromies, numerical and analytic checks; v2: added refs, fixed emai

Dark Matter in the Milky Way's Dwarf Spheroidal Satellites

The Milky Way's dwarf spheroidal satellites include the nearest, smallest and least luminous galaxies known. They also exhibit the largest discrepancies between dynamical and luminous masses. This article reviews the development of empirical constraints on the structure and kinematics of dSph stellar populations and discusses how this phenomenology translates into constraints on the amount and distribution of dark matter within dSphs. Some implications for cosmology and the particle nature of dark matter are discussed, and some topics/questions for future study are identified.Comment: A version with full-resolution figures is available at http://www.cfa.harvard.edu/~mwalker/mwdsph_review.pdf; 70 pages, 22 figures; invited review article to be published in Vol. 5 of the book "Planets, Stars, and Stellar Systems", published by Springe

Dominance of biologically produced nitrate in upland waters of Great Britain indicated by stable isotopes

Atmospheric deposition of nitrogen (N) compounds is the major source of anthropogenic N to most upland ecosystems, where leaching of nitrate (NO3−) into surface waters contributes to eutrophication and acidification as well as indicating an excess of N in the terrestrial catchment ecosystems. Natural abundance stable isotopes ratios, 15N/14N and 18O/16O (the “dual isotope” technique) have previously been used in biogeochemical studies of alpine and forested ecosystems to demonstrate that most of the NO3− in upland surface waters has been microbially produced. Here we present an application of the technique to four moorland catchments in the British uplands including a comparison of lakes and their stream inflows at two sites. The NO3− concentrations of bulk deposition and surface waters at three sites are very similar. While noting the constraints imposed by uncertainty in the precise δ18O value for microbial NO3−, however, we estimate that 79–98% of the annual mean NO3− has been microbially produced. Direct leaching of atmospheric NO3− is a minor component of catchment NO3− export, although greater than in many similar studies in forested watersheds. A greater proportion of atmospheric NO3− is seen in the two lake sites relative to their inflow streams, demonstrating the importance of direct NO3− deposition to lake surfaces in catchments where terrestrial ecosystems intercept a large proportion of deposited N. The dominance of microbial sources of NO3− in upland waters suggests that reduced and oxidised N deposition may have similar implications in terms of contributing to NO3− leaching