Power Spectrum Sensitivity and the Design of Epoch of Reionization Observatories

Recent theoretical developments for observing the Epoch of Reionization (EOR) have concentrated on the power spectrum signature of redshifted 21 cm emission. These studies have demonstrated the great potential of statistical EOR observations, however, the sensitivity calculations for proposed low frequency radio arrays have been highly approximate. The formalism developed for interferometric measurements of the cosmic microwave background can be extended to three dimensions to naturally incorporate the line-of-sight information inherent in the EOR signal. In this paper we demonstrate how to accurately calculate the EOR power spectrum sensitivity of an array, and develop scaling relationships which can be used to guide the design of EOR observatories. The implications for antenna distribution, antenna size, and correlator requirements on the EOR sensitivity are detailed.Comment: 7 pages, 3 figures, submitted to Ap

Wilson Loops and Chiral Correlators on Squashed Sphere

We study chiral deformations of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories obtained by turning on $\tau_J \,{\rm tr} \, \Phi^J$ interactions with $\Phi$ the ${\cal N}=2$ superfield. Using localization, we compute the deformed gauge theory partition function $Z(\vec\tau|q)$ and the expectation value of circular Wilson loops $W$ on a squashed four-sphere. In the case of the deformed ${\cal N}=4$ theory, exact formulas for $Z$ and $W$ are derived in terms of an underlying $U(N)$ interacting matrix model replacing the free Gaussian model describing the ${\cal N}=4$ theory. Using the AGT correspondence, the $\tau_J$-deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as $\tau$-derivatives of the gauge theory partition function on a finite $\Omega$-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the $\epsilon$-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that $SU(2)$ gauge theories on rational $\Omega$-backgrounds are dual to CFT minimal models.Comment: 33 pages, 2 figure, in this version we have added two new references and a detailed comparison with the results obtained in one of these tw

Technological Progress and the Distribution of Productivities across Sectors

This paper studies the impact of the process of technological change on the distribution of productivities and profits across sectors. We find that if technological progress affects high-tech and traditional sectors differently, the impact of changes in the determinants of economic growth may differ depending on which is the actual change. When an economy is growing faster due to an increase in the productivity of research or to a reduction of the taxes on capital accumulation, inequality will decrease. However, if faster growth is due to the presence of tax incentives to high technology sectors or to structural changes that allow a better absorption of externalities, inequality will increase.

Bubbling AdS3

In the light of the recent Lin, Lunin, Maldacena (LLM) results we investigate 1/2-BPS geometries in minimal (and next-to minimal) supergravity in D=6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a two-torus T^2 specified by two harmonic functions. For a rectangular torus the two functions are related by a non-linear equation with rare solutions: AdS_3x S^3, the pp-wave and the multi-center string. ``Bubbling'', i.e. superpositions of droplets, is accommodated by allowing the complex structure of the T^2 to vary over the base. The analysis is repeated in the presence of a tensor multiplet and similar conclusions are reached with generic solutions describing D1D5 (or their dual fundamental string-momentum) systems. In this framework, the profile of the dual fundamental string-momentum system is identified with the boundaries of the droplets in a two-dimensional plane.Comment: 20 pages, 4 figures. v3: Minor corrections in section 2.

RG-flows and Open/Closed String Duality

We discuss the interpaly between IR and UV divergences in theories with open and unoriented strings in view of the AdS/CFT correspondence. We start by deriving general formulas for the computation of threshold corrections to gauge couplings in generic configurations with open and unoriented strings. These allow us to discuss the IR/UV correspondence between beta-function coefficients and ``dilaton'' tadpoles for several brane configurations probed by D3-branes. Finally we comment on the AdS supergravity descriptions of gauge theories that are (super)conformal in the large N limit.Comment: Minor corrections. References added. Version to be published in JHEP08(2000)035. 22 pages, Late

Anomalies & Tadpoles

We show that massless RR tadpoles in vacuum configurations with open and unoriented strings are always related to anomalies. RR tadpoles arising from sectors of the internal SCFT with non-vanishing Witten index are in one-to-one correspondence with conventional irreducible anomalies. The anomalous content of the remaining RR tadpoles can be disclosed by considering anomalous amplitudes with higher numbers of external legs. We then provide an explicit parametrization of the anomaly polynomial in terms of the boundary reflection coefficients, i.e. one-point functions of massless RR fields on the disk. After factorization of the reducible anomaly, we extract the relevant WZ couplings in the effective lagrangians.Comment: 20 pages, Late