Second order equilibrium transport in strongly coupled $$ \mathcal{N} $$ = 4 supersymmetric SU(Nc) Yang-Mills plasma via holography

A relativistic fluid in 3+1 dimensions with a global U(1) symmetry admits nine independent static susceptibilities at the second order in the hydrodynamic derivative expansion, which capture the response of the fluid in thermal equilibrium to the presence of external time-independent sources. Of these, seven are time-reversal $$ \mathbbm{T} $$ T invariant and can be obtained from Kubo formulas involving equilibrium two-point functions of the energy-momentum tensor and the U(1) current. Making use of the gauge/gravity duality along with the aforementioned Kubo formulas, we compute all seven $$ \mathbbm{T} $$ T invariant second order susceptibilities for the $$ \mathcal{N} $$ N = 4 supersymmetric SU(Nc) Yang-Mills plasma in the limit of large Nc and at strong ’t-Hooft coupling λ. In particular, we consider the plasma to be charged under a U(1) subgroup of the global SU(4) R-symmetry of the theory. We present analytic expressions for three of the seven $$ \mathbbm{T} $$ T invariant susceptibilities, while the remaining four are computed numerically. The dual gravitational description for the charged plasma in thermal equilibrium in the absence of background electric and magnetic fields is provided by the asymptotically AdS5 Reissner-Nordström black brane geometry. The susceptibilities are extracted by studying perturbations to the bulk geometry as well as to the bulk gauge field. We also present an estimate of the second order transport coefficient κ, which determines the response of the fluid to the presence of background curvature, for QCD, and compare it with previous determinations made using different techniques.

Extended General Relativity for a Conformally Curved Universe

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses a positively curved early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with Quantum Mechanics and the necessity of dark matter/energy could indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents extended field equations by considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which can remove singularities, satisfy a conformal invariance theory and facilitate its quantisation.

Extended General Relativity for a Curved Universe

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB). Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses the positive curvature of the early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with quantum mechanics and the necessity of dark matter and dark energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this study presents extended field equations considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which could remove singularities from the theory and facilitate its quantisation. The extended equations have been utilised to derive the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature.

Derivative couplings in gravitational production in the early universe

Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term. The most general first order action contains derivative couplings to the curvature scalar and to the traceless Ricci tensor, which can be dominant in the case of (pseudo-)Nambu-Goldstone bosons or disformal scalars, such as branons. In the presence of these derivative couplings, the density of produced particles for the adiabatic regime in the de Sitter phase (which mimics inflation) is constant in time and decays with the inverse effective mass (which in turn depends on the coupling to the curvature scalar). In the reheating phase following inflation, the presence of derivative couplings to the background curvature modifies in a nontrivial way the gravitational production even in the perturbative regime. We also show that the two couplings — to the curvature scalar and to the traceless Ricci tensor — are drastically different, specially for large masses. In this regime, the production becomes highly sensitive to the former coupling while it becomes independent of the latter.

Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?

The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the “extended uncertainty principle” (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de Sitter case). We compare the results with previous works in the EUP literature, which are not all consistent. Our result further highlights an important issue in the literature of generalizations of the uncertainty principle: how much can heuristic derivations be trusted?

Gravitational waves in modified Gauss–Bonnet gravity

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

Specific heat of 2D interacting Majorana fermions from holography

Majorana fermions are a fascinating medium for discovering new phases of matter. However, the standard analytical tools are very limited in probing the non-perturbative aspects of interacting Majoranas in more than one dimensions. Here, we employ the holographic correspondence to determine the specific heat of a two-dimensional interacting gapless Majorana system. To perform our analysis we first describe the interactions in terms of a pseudo-scalar torsion field. We then allow fluctuations in the background curvature thus identifying our model with a (2 + 1)-dimensional Anti-de Sitter (AdS) geometry with torsion. By employing the AdS/CFT correspondence, we show that the interacting model is dual to a (1 + 1)-dimensional conformal field theory (CFT) with central charge that depends on the interaction coupling. This non-perturbative result enables us to determine the effect interactions have in the specific heat of the system at the zero temperature limit.

Multipoint Background Analysis: Gaining Precision and Accuracy in Microprobe Trace Element Analysis

Electron microprobe trace element analysis is a significant challenge. Due to the low net intensity of peak measurements, the accuracy and precision of such analyses relies critically on background measurements, and on the accuracy of any pertinent peak interference corrections. A linear regression between two points selected at appropriate background positions is a classical approach for electron probe microanalysis (EPMA). However, this approach neglects the accurate assessment of background curvature (exponential or polynomial), and the presence of background interferences, a hole in the background, or an absorption edge can dramatically affect the results if underestimated or ignored. The acquisition of a quantitative wavelength-dispersive spectrometry (WDS) scan over the spectral region of interest remains a reasonable option to determine the background intensity and curvature from a fitted regression of background portions of the scan, but this technique can be time consuming and retains an element of subjectivity, as the analyst has to select areas in the scan which appear to represent background. This paper presents a new multi-point background (MPB) method whereby the background intensity is determined from up to 24 background measurements from wavelength positions on either side of analytical lines. This method improves the accuracy and precision of trace element analysis in a complex matrix through careful regression of the background shape, and can be used to characterize the background over a large spectral region covering several elements to be analyzed. The overall efficiency improves as systematic WDS scanning is not required to assess background interferences. The method is less subjective compared to methods that rely on WDS scanning, including selection of two interpolation points based on WDS scans, because “true” backgrounds are selected through an exclusion method of possible erroneous backgrounds. The first validation of the MPB method involves blank testing to ensure the method can accurately measure the absence of an element. The second validation involves the analysis of U-Th-Pb in several monazite reference materials of known isotopic age. The impetus for the MPB method came from efforts to refine EPMA monazite U-Th-Pb dating, where it was recognized that background errors resulting from interference or strong background curvature could result in errors of several tens of millions of years on the calculated date. Results obtained on monazite reference materials using two different microprobes, a Cameca SX-100 Ultrachron and a JEOL JXA-8230, yield excellent agreement with ages obtained by isotopic methods (Thermal Ionization Mass Spectrometry [TIMS], Sensitive High-Resolution Ion MicroProbe [SHRIMP], or Secondary Ion Mass Spectrometry [SIMS]). Finally, the MPB method can be used to model the background over a large spectrometer range to improve the accuracy of background measurement of minor and trace elements acquired on a same spectrometer, a method called the shared background measurement. This latter significantly improves the accuracy of minor and trace element analysis in complex matrices, as demonstrated by the analysis of Rare Earth Elements (REE) in REE-silicates and phosphates and of trace elements in scheelite.

Quantum corrections to the geodesic equation

The geodesic equation of motion for a particle moving in a background gravitational field can be derived from an action that is essentially that of a one-dimensional bosonic nonlinear sigma model. We quantize the particle, and obtain its effective action to lowest order in both the background curvature and the loop expansion, using the background quantization procedure appropriate to the nonlinear sigma model. Operator regularization is used to regulate the theory. Explicit calculation shows that these lowest order corrections vanish exactly.

Background Correction in Raman Spectroscopic Determination of Dimethylsulfone, Sulfate, and Bisulfate

A study has been made to compare the effectiveness of thirteen methods of spectroscopic background correction in quantitative measurements. These include digital filters, least-squares fitting, and cross-correlation, as well as peak area and height measurements. Simulated data sets with varying S/N and degrees of background curvature were used. The results were compared with the results of corresponding treatments of Raman spectra of dimethyl sulfone, sulfate, and bisulfate. The range of variation of the simulated sets was greater than was possible with the experimental data, but where conditions were comparable, the agreement between them was good. This supports the conclusion that the simulations were valid. Best results were obtained by a least-squares fit with the use of simple polynomials to generate the background correction. Under the conditions employed, limits of detection were about 80 ppm for dimethyl sulfone and sulfate and 420 ppm for bisulfate.