Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

The alpha-effect in rotating convection: a comparison of numerical simulations

Numerical simulations are an important tool in furthering our understanding of turbulent dynamo action, a process that occurs in a vast range of astrophysical bodies. It is important in all computational work that comparisons are made between different codes and, if non-trivial differences arise, that these are explained. Kapyla et al (2010: MNRAS 402, 1458) describe an attempt to reproduce the results of Hughes & Proctor (2009: PRL 102, 044501) and, by employing a different methodology, they arrive at very different conclusions concerning the mean electromotive force and the generation of large-scale fields. Here we describe why the simulations of Kapyla et al (2010) are simply not suitable for a meaningful comparison, since they solve different equations, at different parameter values and with different boundary conditions. Furthermore we describe why the interpretation of Kapyla et al (2010) of the calculation of the alpha-effect is inappropriate and argue that the generation of large-scale magnetic fields by turbulent convection remains a problematic issue.Comment: Submitted to MNRAS. 5 pages, 3 figure

Observables in the equivariant A-model

We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: the first one is conjectured to compute the correlators of the A-model with target the Marsden-Weinstein reduced space; in the second one we recover the topological Yang-Mills action coupled with A-model so that the A-model observables are closed under supersymmetry.Comment: 16 pages; minor correction

Classical BV theories on manifolds with boundary

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the $BF$ theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.Comment: The second version has many typos corrected, references added. Some typos are probably still there, in particular, signs in examples. In the third version more typoes are corrected and the exposition is slightly change

The Relative Space: Space Measurements on a Rotating Platform

We introduce here the concept of relative space, an extended 3-space which is recognized as the only space having an operational meaning in the study of the space geometry of a rotating disk. Accordingly, we illustrate how space measurements are performed in the relative space, and we show that an old-aged puzzling problem, that is the Ehrenfest's paradox, is explained in this purely relativistic context. Furthermore, we illustrate the kinematical origin of the tangential dilation which is responsible for the solution of the Ehrenfest's paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of Physic

Galaxy bulges and their black holes: a requirement for the quenching of star formation

One of the central features of the last 8 to 10 billion years of cosmic history has been the emergence of a well-populated red sequence of non-star-forming galaxies. A number of models of galaxy formation and evolution have been devised to attempt to explain this behavior. Most current models require feedback from supermassive black holes (AGN feedback) to quench star formation in galaxies in the centers of their dark matter halos (central galaxies). Such models make the strong prediction that all quenched central galaxies must have a large supermassive black hole (and, by association, a prominent bulge component). I show using data from the Sloan Digital Sky Survey that the observations are consistent with this prediction. Over 99.5% of red sequence galaxies with stellar masses in excess of 10^{10} M_{\sun} have a prominent bulge component (as defined by having a Sersic index n above 1.5). Those very rare red sequence central galaxies with little or no bulge (n<1.5) usually have detectable star formation or AGN activity; the fraction of truly quenched bulgeless central galaxies is <0.1% of the total red sequence population. I conclude that a bulge, and by implication a supermassive black hole, is an absolute requirement for full quenching of star formation in central galaxies. This is in agreement with the most basic prediction of the AGN feedback paradigm.Comment: 6 pages, 4 color figures (figure 1 is of slightly degraded quality). To appear in August 1 edition of the Astrophysical Journa

Social Interactions and Schooling Decisions

The aim of this paper is to study whether a child's schooling choices are affected by the schooling choices of other children. Identification is based on a randomized targeted intervention that grants a cash subsidy conditional on school attendance to a subgroup of eligible children within small rural villages in Mexico (PROGRESA). This policy change spills over to ineligible children if social interactions are relevant. Results indicate that the eligible children tend to attend school more frequently, and the ineligible children acquire more schooling when the subsidy is introduced in their local village. Moreover, the overall effect of PROGRESA on eligible children is the sum of a direct effect due to cash transfers and an indirect effect due to changes in peer group schooling. Interestingly, the social interactions effect is almost as important as the direct effect

Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.