Concerning LpL^p resolvent estimates for simply connected manifolds of constant curvature

We prove families of uniform $(L^r,L^s)$ resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean space of Kenig, Ruiz and the second author \cite{KRS}. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem.Comment: 25 pages, 2 figure

How good are your testers? An assessment of testing ability

During our previous research conducted in the Sheffield Software Engineering Observatory [11], we found that test first programmers spent a higher percentage of their time testing than those testing after coding. However as the team allocation was based on subjects' academic records and their preference, it was unclear if they were simply better testers. Thus this paper proposes two questionnaires to assess the testing ability of subjects, in order to reveal the factors that contribute to the previous findings. Preliminary results show that the testing ability of subjects, as measured by the survey, varies based on their professional skill level

Boundary Conformal Field Theory and a Boundary Central Charge

We consider the structure of current and stress tensor two-point functions in conformal field theory with a boundary. The main result of this paper is a relation between a boundary central charge and the coefficient of a displacement operator correlation function in the boundary limit. The boundary central charge under consideration is the coefficient of the product of the extrinsic curvature and the Weyl curvature in the conformal anomaly. Along the way, we describe several auxiliary results. Three of the more notable are as follows: (1) we give the bulk and boundary conformal blocks for the current two-point function; (2) we show that the structure of these current and stress tensor two-point functions is essentially universal for all free theories; (3) we introduce a class of interacting conformal field theories with boundary degrees of freedom, where the interactions are confined to the boundary. The most interesting example we consider can be thought of as the infrared fixed point of graphene. This particular interacting conformal model in four dimensions provides a counterexample of a previously conjectured relation between a boundary central charge and a bulk central charge. The model also demonstrates that the boundary central charge can change in response to marginal deformations.Comment: 75 pages, 4 figures; v2: references added. v3: comments on anomalous dimension and references added. v4: minor corrections, published versio

Interface Conformal Anomalies

We consider two $d \geq 2$ conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we compute the heat kernel coefficients and interface central charges in free theories. The results are consistent with the known boundary CFT data via the folding trick. In $d=4$, two interface invariants generally allowed as anomalies turn out to have vanishing interface charges. These missing invariants are constructed from components with odd parity with respect to flipping the orientation of the defect. We conjecture that all invariants constructed from components with odd parity may have vanishing coefficient for symmetric interfaces, even in the case of interacting interface CFT.Comment: 14 pp; v2: clarifications added, introduction expande

Physical Correlations of the Scatter between Galaxy Mass, Stellar Content, and Halo Mass

We use the UniverseMachine to analyze the source of scatter between the central galaxy mass, the total stellar mass in the halo, and the dark matter halo mass. We also propose a new halo mass estimator, the cen+N mass: the sum of the stellar mass of the central and the N most massive satellites. We show that, when real space positions are perfectly known, the cen+N mass has scatter competitive with that of richness-based estimators. However, in redshift space, the cen+N mass suffers less from projection effects in the UniverseMachine model. The cen+N mass is therefore a viable low scatter halo mass estimator, and should be considered an important tool to constrain cosmology with upcoming spectroscopic data from DESI. We analyze the scatter in stellar mass at fixed halo mass and show that the total stellar mass in a halo is uncorrelated with secondary halo properties, but that the central stellar mass is a function of both halo mass and halo age. This is because central galaxies in older halos have had more time to grow via accretion. If the UniverseMachine model is correct, accurate galaxy-halo modeling of mass selected samples therefore needs to consider halo age in addition to mass.Comment: 13 pages, 11 figures, submitted to MNRA

Superconformal Models for Graphene and Boundary Central Charges

In the context of boundary conformal field theory, we investigate whether the boundary trace anomaly can depend on marginal directions in the presence of supersymmetry. Recently, it was found that a graphene-like non-supersymmetric conformal field theory with a four-dimensional bulk photon and a three-dimensional boundary electron has two boundary central charges that depend on an exactly marginal direction, namely the gauge coupling. In this work, we supersymmetrize this theory, paying special attention to the boundary terms required by supersymmetry. We study models with 4, 8, and 16 Poincar\'e supercharges in the bulk, half of which are broken by the boundary. In all cases, we find that at all orders in perturbation theory, the gauge coupling is not renormalized, providing strong evidence that these theories are boundary conformal field theories. Moreover, the boundary central charges depend on the coupling. One possible exception to this dependence on marginal directions is that the difference between the two charges is coupling independent at one-loop in the maximally supersymmetric case. In our analysis, a possible boundary Chern-Simons term is incorporated by a bulk $\theta$-term.Comment: 47 pages; v2: footnotes and references adde