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

Wrapped sheaves

We construct a sheaf-theoretic analogue of the wrapped Fukaya category in Lagrangian Floer theory, by localizing a category of sheaves microsupported away from some given $\Lambda \subset S^*M$ along continuation maps constructed using the Guillermou-Kashiwara-Schapira sheaf quantization. When $\Lambda$ is a subanalytic singular isotropic, we also construct a comparison map to the category of compact objects in the category of unbounded sheaves microsupported in $\Lambda$, and show that it is an equivalence. The last statement can be seen as a sheaf theoretical incarnation of the sheaf-Fukaya comparison theorem of Ganatra-Pardon-Shende.Comment: 54 pages, 4 figure

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

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

Anodic dissolution of lead in aqueous solutions

The apparent valence of lead was determined in one normal solutions of potassium nitrate, ammonium acetate, lead nitrate, and lead acetate at temperatures of 25 and 50°C. The current density was varied from 0.001 to 1.00 amp•cm -2. The apparent valence of lead ranged between 1.90 and 2.00 in all solutions. The lower valences were reached at higher current densities. The amount of disintegration was very small, and was dependent upon film formation on the surface of the anode. Potential-current density relationships for the anodic dissolution of lead were obtained in the electrolytes mentioned above. In potassium nitrate and ammonium acetate solutions, the Tafel slopes were 0.030 volts. The proposed dissolution mechanism is Pb(s) → Pb+(s) + e (fast) Pb+(s) → Pb+2(s) + e (fast) Pb+2(s) → Pb+2(aq) (slow) --Abstract, page ii

A study of the anodic oxidation of acetylene on platinum-gold alloys

The anodic oxidation of acetylene on Pt-Au alloys of four compositions (80-20, 60-40, 40-60, and 20-80 Pt-Au) was studied at 80°C in solutions of constant pH and unit normality. Currents were measured as a function of potential and partial pressure of acetylene. The effects of temperature on current in 1 N H₂SO₄ and 1 N NaOH and the coulombic efficiencies for CO₂ production were determined. The experimental results indicated that the alloys can be classified into three groups, Pt-rich, Au-rich, and intermediate compositions. A transition region (change of the mechanism) was found for the Au-rich alloys. The oxidation can be interpreted in terms of two mechanisms...The total current on the heterogeneous phases can be represented as the sum of the currents on the phases --Abstract, page ii-iii

Duality and spherical adjunction from microlocalization -- An approach by contact isotopies

For a subanalytic Legendrian $\Lambda \subset S^{*}M$, we prove that when $\Lambda$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_\Lambda: \operatorname{Sh}_\Lambda(M) \rightarrow \operatorname{\mu sh}_\Lambda(\Lambda)$ is a spherical functor, and the spherical cotwist is the Serre functor on the subcategory $\operatorname{Sh}_\Lambda^b(M)_0$ of compactly supported sheaves with perfect stalks. In this case, when $M$ is compact the Verdier duality on $\operatorname{Sh}_\Lambda^b(M)$ extends naturally to all compact objects $\operatorname{Sh}_\Lambda^c(M)$. This is a sheaf theory counterpart (with weaker assumptions) of the results on the cap functor and cup functors between Fukaya categories. When proving spherical adjunction, we deduce the Sato-Saboff fiber sequence and construct the Guillermou doubling functor for any Reeb flow. As a setup for the Verdier duality statement, we study the dualizability of $\operatorname{Sh}_\Lambda(M)$ itself and obtain a classification result of colimit-preserving functors by convolutions of sheaf kernels.Comment: 74 pages, 5 figures. A new discussion around Proposition 4.1

The Forgotten Children

The “forgotten children” of pediatric cancer are the siblings. There is a dearth of literature published on the effects of cancer on the siblings’ psychosocial state. Despite significant improvements made in the survival of pediatric cancer patients, the psychosocial health of the siblings remains the same. The siblings’ need for support and understanding continue to go unnoticed. The aim of this chapter is to shed light on the roles siblings play in the pediatric cancer trajectory, as well as to recognize the emotional and psychological toll they endure through the experience of diagnosis, treatment, survival, and bereavement as the “forgotten children.

The variability of currents and sea level in the upper Delaware estuary

The variability of currents and sea levels in the upper Delaware estuary are examined based on measurements from bottom mounted acoustic Doppler current profilers (ADCP) deployed at two sites (New Castle and Tinicum) from 18 March to 10 June 2003. New Castle is located 104 km from the mouth, and Tinicum is located another 32 km up-estuary. Supplemental data, including sea level at the mouth of the estuary, river discharge, and wind speed and direction, were also obtained from various federal agencies. The instantaneous current represents a superposition of variability driven by the tide, wind, and river discharge. Over the short (\u3c36 hr) time scale, the tide is the dominant forcing mechanism, with M2 being the principal tidal constituent. The amplitude of the M2 tide increases from the mouth to the upper estuary and gives rise to a vigorous M2 current of the order 80 cm s–1. On time scales of 36 to 120 hr, the effect of wind drives a weak subtidal current with a standard deviation of 2 cm s–1 in the upper estuary. At time scales longer than 120 hr, the subtidal current variability, with a standard deviation of 6 cm s–1, is dominated by the barotropic response of the upper estuary to variations in the river discharge. The upper estuary exhibits a strong down-estuary mean current of the order—15 cm s–1. At Tinicum, river discharge accounts for more than half of the mean current, which is characterized by down-estuary flow throughout the water column. The magnitude of the river discharge-induced mean current is reduced at New Castle, in direct response to the down-estuary increase in the cross-sectional area. Tidally rectified current accounts for the remainder of the overall mean flow at Tinicum, and the effect of tidal rectification may be more important than river discharge in producing the mean flow at New Castle. There is no evidence of a baroclinic gravitational circulation, as the salt intrusion generally does not extend into the upper estuary