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1. Quantum group intertwiner space from quantum curved tetrahedron

   https://doi.org/10.1088/1361-6382/ad5f71  

   Han, Muxin; Hsiao, Chen-Hung; Pan, Qiaoyin (July 2024, Classical and Quantum Gravity)

   Abstract In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in Haggardet al(2016Ann. Henri Poincaré172001–48). Our method is based on the relation between this phase space and the moduli space of SU(2) flat connections on a 4-punctured sphere. The quantization results in the physical Hilbert space as the solution of the quantum closure constraint, which quantizes the classical closure condition $M_4{M}_3{M}_2{M}_1=1$, $M_{\nu }\in \mathrm{SU}\left(2\right)$, for the homogeneously curved tetrahedron. The quantum group $U_q\left(\mathfrak{su}\right(2\left)\right)$emerges as the gauge symmetry of a quantum tetrahedron. The physical Hilbert space of the quantum tetrahedron coincides with the Hilbert space of 4-valent intertwiners of $U_q\left(\mathfrak{su}\right(2\left)\right)$. In addition, we define the area operators quantizing the face areas of the tetrahedron and compute the spectrum. The resulting spectrum is consistent with the usual Loop-Quantum-Gravity area spectrum in the large spin regime but is different for small spins. This work closely relates to 3+1 dimensional Loop Quantum Gravity in presence of cosmological constant and provides a justification for the emergence of quantum group in the theory. 

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2. Planck Dust Polarization Power Spectra Are Consistent with Strongly Supersonic Turbulence

   https://doi.org/10.3847/1538-4357/ad571b  

   Stalpes, Kye_A; Collins, David_C; Huffenberger, Kevin_M (August 2024, The Astrophysical Journal)

   Abstract The polarization of the cosmic microwave background is rich in information but obscured by foreground emission from the Milky Way’s interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, ${\mathcal{M}}_{\mathcal{S}}$, and magnetic (Alfvén) Mach number, ${\mathcal{M}}_{\mathrm{A}}$. We measure the power spectra of density (ρ), velocity (v), magnetic field (H), total projected intensity (T), parity-even polarization (E), and parity-odd polarization (B). We find that the slopes of all six quantities increase with ${\mathcal{M}}_{\mathcal{S}}$. Most increase with ${\mathcal{M}}_{\mathrm{A}}$, while the magnetic field spectrum steepens with ${\mathcal{M}}_{\mathrm{A}}$. By comparing spectral slopes ofEandBto those measured by Planck, we infer typical values of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$for the ISM. As the fluid velocity increases, ${\mathcal{M}}_{\mathcal{S}}>4$, the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ∼0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find thatr^TE≈ 0.3, in agreement with Planck, for appropriate combinations of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$. Finally, we consider parity-violating correlationsr^TBandr^EB. 

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3. Test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$ and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$ decays in proton-proton collisions at $\sqrt{\text{s}}=\text{13}\text{TeV}$

   https://doi.org/10.1088/1361-6633/ad4e65  

   CMS_Collaboration, The (July 2024, Reports on Progress in Physics)

   Abstract A test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$decays, as well as a measurement of differential and integrated branching fractions of a nonresonant ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}=13\text{TeV}$recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})$to $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-})$is determined from the measured double ratio $R\left(\text{K}\right)$of these decays to the respective branching fractions of the ${\text{B}}^{\pm }\to \text{J}/\text{ψ}{\text{K}}^{\pm }$with $\text{J}/\text{ψ}\to {\mu }^{+}{\mu }^{-}$and ${\text{e}}^{+}{\text{e}}^{-}$decays, which allow for significant cancellation of systematic uncertainties. The ratio $R\left(\text{K}\right)$is measured in the range $1.1<q^2<6.0{\text{GeV}}^2$, whereqis the invariant mass of the lepton pair, and is found to be $R\left(\text{K}\right)={0.78}_{-0.23}^{+0.47}$, in agreement with the standard model expectation $R\left(\text{K}\right)\approx 1$. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the sameq²range, $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})=(12.42\pm 0.68)\times {10}^{-8}$, is consistent with the present world-average value and has a comparable precision. 

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4. On the generalization of the Kruskal–Szekeres coordinates: a global conformal charting of the Reissner–Nordström spacetime

   https://doi.org/10.1088/1361-6382/ad4dff  

   Aly, Fawzi; Stojkovic, Dejan (May 2024, Classical and Quantum Gravity)

   Abstract The Kruskal–Szekeres coordinate construction for the Schwarzschild spacetime could be interpreted simply as a squeezing of thet-line into a single point, at the event horizon $r=2M$. Starting from this perspective, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner–Nordström manifold, $M_{\text{RN}}$. We develop a new method to construct Kruskal-like coordinates through casting the metric in new null coordinates, and find two algebraically distinct ways to chart $M_{\text{RN}}$, referred to as classes: type-I and type-II within this work. We pedagogically illustrate our method by crafting two compact, conformal, and global coordinate systems labeled ${\mathrm{GK}}_{\text{I}}$and ${\mathrm{GK}}_{\text{II}}$as an example for each class respectively, and plot the corresponding Penrose diagrams. In both coordinates, the metric differentiability can be promoted to $C^{\mathrm{\infty }}$in a straightforward way. Finally, the conformal metric factor can be written explicitly in terms of thetandrfunctions for both types of charts. We also argued that the chart recently reported in Soltani (2023 arXiv:2307.11026) could be viewed as another example for the type-II classification, similar to ${\mathrm{GK}}_{\text{II}}$. 

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5. Stable phase retrieval and perturbations of frames

   https://doi.org/10.1090/bproc/185  

   Alharbi, Wedad; Freeman, Daniel; Ghoreishi, Dorsa; Lois, Claire; Sebastian, Shanea (September 2023, Proceedings of the American Mathematical Society, Series B)

   Dilworth, Stephen (Ed.)

   A frame $(x_j{)}_{j\in <\#comment/>J}$for a Hilbert space $H$is said to do phase retrieval if for all distinct vectors $x,y\in <\#comment/>H$the magnitudes of the frame coefficients $(|⟨<\#comment/>x,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$and $(|⟨<\#comment/>y,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$distinguish $x$from $y$(up to a unimodular scalar). A frame which does phase retrieval is said to do $C$-stable phase retrieval if the recovery of any vector $x\in <\#comment/>H$from the magnitude of the frame coefficients is $C$-Lipschitz. It is known that if a frame does stable phase retrieval then any sufficiently small perturbation of the frame vectors will do stable phase retrieval, though with a slightly worse stability constant. We provide new quantitative bounds on how the stability constant for phase retrieval is affected by a small perturbation of the frame vectors. These bounds are significant in that they are independent of the dimension of the Hilbert space and the number of vectors in the frame. 

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