Absolute conservation law for black holes

In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric and in a Bondi-Sachs metric using the first order formulation of spherically reduced gravity, which allows easy and direct fixations of any type of gauge. The relation of our conserved quantity to the ADM and Bondi mass is investigated. Further possible applications (ideal fluid, black holes in higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.

The Three-point Function in Split Dimensional Regularization in the Coulomb Gauge

We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\Sigma (p)$ and quark-quark-gluon vertex function $\Lambda_\mu (p^\prime,p)$ in the Coulomb gauge, $\vec{\bigtriangledown}\cdot\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $\omega$ and $\sigma$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $\Sigma$ and $\Lambda_\mu$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $\Sigma$ and $\Lambda_\mu$ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed.Comment: Latex, 17 pages, 4 figures, uses epsf.sty, epsfig.sty; to appear in Nuc. Phys.

Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters \sigma and n/2-\sigma for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for \Sigma(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit \sigma \to 1/2 and the subleading terms in the epsilon-expansion of noncovariant integrals.Comment: 32 pages Latex; figures replaced, text unchange

Universal conservation law and modified Noether symmetry in 2d models of gravity with matter

It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines the global classification of all (classical) solutions. For the special case of spherically reduced Einstein gravity it coincides with the mass in the Schwarzschild solution. The corresponding Noether symmetry has been derived previously by P. Widerin and one of the authors (W.K.) for a specific 2d model with nonvanishing torsion. In the present paper this is generalized to all covariant 2d theories, including interactions with matter. The related Noether-like symmetry differs from the usual one. The parameters for the symmetry transformation of the geometric part and those of the matterfields are distinct. The total conservation law (a zero-form current) results from a two stage argument which also involves a consistency condition expressed by the conservation of a one-form matter ``current''. The black hole is treated as a special case.Comment: 3

Similar temperature scale for valence changes in Kondo lattices with different Kondo temperatures

The Kondo model predicts that both the valence at low temperatures and its temperature dependence scale with the characteristic energy T_K of the Kondo interaction. Here, we study the evolution of the 4f occupancy with temperature in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In agreement with simple theoretical models, we observe a scaling between the valence at low temperature and T_K obtained from thermodynamic measurements. In contrast, the temperature scale T_v at which the valence increases with temperature is almost the same in all investigated materials while the Kondo temperatures differ by almost four orders of magnitude. This observation is in remarkable contradiction to both naive expectation and precise theoretical predictions of the Kondo model, asking for further theoretical work in order to explain our findings. Our data exclude the presence of a quantum critical valence transition in YbRh2Si2

High-energy magnetic excitations in overdoped La2−x_{2-x}Srx_{x}CuO4_{4} studied by neutron and resonant inelastic X-ray scattering

We have performed neutron inelastic scattering and resonant inelastic X-ray scattering (RIXS) at the Cu-$L_3$ edge to study high-energy magnetic excitations at energy transfers of more than 100 meV for overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.25$ ($T_c=15$ K) and $x=0.30$ (non-superconducting) using identical single crystal samples for the two techniques. From constant-energy slices of neutron scattering cross-sections, we have identified magnetic excitations up to ~250 meV for $x=0.25$. Although the width in the momentum direction is large, the peak positions along the (pi, pi) direction agree with the dispersion relation of the spin-wave in the non-doped La$_{2}$CuO$_{4}$ (LCO), which is consistent with the previous RIXS results of cuprate superconductors. Using RIXS at the Cu-$L_3$ edge, we have measured the dispersion relations of the so-called paramagnon mode along both (pi, pi) and (pi, 0) directions. Although in both directions the neutron and RIXS data connect with each other and the paramagnon along (pi, 0) agrees well with the LCO spin-wave dispersion, the paramagnon in the (pi, pi) direction probed by RIXS appears to be less dispersive and the excitation energy is lower than the spin-wave of LCO near (pi/2, pi/2). Thus, our results indicate consistency between neutron inelastic scattering and RIXS, and elucidate the entire magnetic excitation in the (pi, pi) direction by the complementary use of two probes. The polarization dependence of the RIXS profiles indicates that appreciable charge excitations exist in the same energy range of magnetic excitations, reflecting the itinerant character of the overdoped sample. A possible anisotropy in the charge excitation intensity might explain the apparent differences in the paramagnon dispersion in the (pi, pi) direction as detected by the X-ray scattering.Comment: 7 pages, 7 figure

Caveolin-3 differentially orchestrates cholinergic and serotonergic constriction of murine airways

The mechanisms of controlling airway smooth muscle (ASM) tone are of utmost clinical importance as inappropriate constriction is a hallmark in asthma and chronic obstructive pulmonary disease. Receptors for acetylcholine and serotonin, two relevant mediators in this context, appear to be incorporated in specialized, cholesterol-rich domains of the plasma membrane, termed caveolae due to their invaginated shape. The structural protein caveolin-1 partly accounts for anchoring of these receptors. We here determined the role of the other major caveolar protein, caveolin-3 (cav-3), in orchestrating cholinergic and serotonergic ASM responses, utilizing newly generated cav-3 deficient mice. Cav-3 deficiency fully abrogated serotonin-induced constriction of extrapulmonary airways in organ baths while leaving intrapulmonary airways unaffected, as assessed in precision cut lung slices. The selective expression of cav-3 in tracheal, but not intrapulmonary bronchial epithelial cells, revealed by immunohistochemistry, might explain the differential effects of cav-3 deficiency on serotonergic ASM constriction. The cholinergic response of extrapulmonary airways was not altered, whereas a considerable increase was observed in cav-3â -/- intrapulmonary bronchi. Thus, cav-3 differentially organizes serotonergic and cholinergic signaling in ASM through mechanisms that are specific for airways of certain caliber and anatomical position. This may allow for selective and site-specific intervention in hyperreactive states

Wilson Loop and the Treatment of Axial Gauge Poles

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that as under the FFBRS transformation the vacuum expectation value of a gauge invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Further, we give an argument for {\it direct} verification of the invariance of Wilson loop to O(g^4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g^2).Comment: 8 pages, LaTex; some typos related to equation (18) correcte

High-resolution resonant inelastic soft X-ray scattering as a probe of the crystal electrical field in lanthanides demonstrated for the case of CeRh2Si2

The magnetic properties of rare earth compounds are usually well captured by assuming a fully localized f shell and only considering the Hund's rule ground state multiplet split by a crystal electrical field (CEF). Currently, the standard technique for probing CEF excitations in lanthanides is inelastic neutron scattering. Here we show that with the recent leap in energy resolution, resonant inelastic soft X-ray scattering has become a serious alternative for looking at CEF excitations with some distinct advantages compared to INS. As an example we study the CEF scheme in CeRh2Si2, a system that has been intensely studied for more than two decades now but for which no consensus has been reached yet as to its CEF scheme. We used two new features that have only become available very recently in RIXS, high energy resolution of about 30 meV as well as polarization analysis in the scattered beam, to find a unique CEF description for CeRh2Si2. The result agrees well with previous INS and magnetic susceptibility measurements. Due to its strong resonant character, RIXS is applicable to very small samples, presents very high cross sections for all lanthanides, and further benefits from the very weak coupling to phonon excitation. The rapid progress in energy resolution of RIXS spectrometers is making this technique increasingly attractive for the investigation of the CEF scheme in lanthanides