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1. When left and right disagree: entropy and von Neumann algebras in quantum gravity with general AlAdS boundary conditions

   https://doi.org/10.1007/JHEP08(2024)010  

   Marolf, Donald; Zhang, Daiming (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Euclidean path integrals for UV-completions ofd-dimensional bulk quantum gravity were recently studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflection-positivity, and factorization. Sectors$$ {\mathcal{H}}_{\mathcal{B}} $$ $H_B$of the resulting Hilbert space were then defined for any (d− 2)-dimensional surface$$ \mathcal{B} $$ $B$, where$$ \mathcal{B} $$ $B$may be thought of as the boundary ∂Σ of a bulk Cauchy surface in a corresponding Lorentzian description, and where$$ \mathcal{B} $$ $B$includes the specification of appropriate boundary conditions for bulk fields. Cases where$$ \mathcal{B} $$ $B$was the disjoint unionB⊔Bof two identical (d− 2)-dimensional surfacesBwere studied in detail and, after the inclusion of finite-dimensional ‘hidden sectors,’ were shown to provide a Hilbert space interpretation of the associated Ryu-Takayanagi entropy. The analysis was performed by constructing type-I von Neumann algebras$$ {\mathcal{A}}_L^B $$ $A_L^B$,$$ {\mathcal{A}}_R^B $$ $A_R^B$that act respectively at the left and right copy ofBinB⊔B. Below, we consider the case of general$$ \mathcal{B} $$ $B$, and in particular for$$ \mathcal{B} $$ $B$=B_L⊔B_RwithB_L,B_Rdistinct. For anyB_R, we find that the von Neumann algebra atB_Lacting on the off-diagonal Hilbert space sector$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ $H_{B_L\bigsqcup B_R}$is a central projection of the corresponding type-I von Neumann algebra on the ‘diagonal’ Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ $H_{B_L\bigsqcup B_L}$. As a result, the von Neumann algebras$$ {\mathcal{A}}_L^{B_L} $$ $A_L^{B_L}$,$$ {\mathcal{A}}_R^{B_L} $$ $A_R^{B_L}$defined in [1] using the diagonal Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ $H_{B_L\bigsqcup B_L}$turn out to coincide precisely with the analogous algebras defined using the full Hilbert space of the theory (including all sectors$$ {\mathcal{H}}_{\mathcal{B}} $$ $H_B$). A second implication is that, for any$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ $H_{B_L\bigsqcup B_R}$, including the same hidden sectors as in the diagonal case again provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. We also show the above central projections to satisfy consistency conditions that lead to a universal central algebra relevant to all choices ofB_LandB_R. 

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2. Characterizing Schwarz maps by tracial inequalities

   https://doi.org/10.1007/s11005-023-01636-4  

   Carlen, Eric; Müller-Hermes, Alexander (February 2023, Letters in Mathematical Physics)

   Abstract Let$$\phi $$ $\varphi$be a positive map from the$$n\times n$$ $n\times n$matrices$$\mathcal {M}_n$$ $M_n$to the$$m\times m$$ $m\times m$matrices$$\mathcal {M}_m$$ $M_m$. It is known that$$\phi $$ $\varphi$is 2-positive if and only if for all$$K\in \mathcal {M}_n$$ $K\in M_n$and all strictly positive$$X\in \mathcal {M}_n$$ $X\in M_n$,$$\phi (K^*X^{-1}K) \geqslant \phi (K)^*\phi (X)^{-1}\phi (K)$$ $\varphi \left(K^{\ast }{X}^{-1}K\right)⩾\varphi {\left(K\right)}^{\ast }\varphi {\left(X\right)}^{-1}\varphi \left(K\right)$. This inequality is not generally true if$$\phi $$ $\varphi$is merely a Schwarz map. We show that the corresponding tracial inequality$${{\,\textrm{Tr}\,}}[\phi (K^*X^{-1}K)] \geqslant {{\,\textrm{Tr}\,}}[\phi (K)^*\phi (X)^{-1}\phi (K)]$$ $\text{Tr}\left[\varphi \left(K^{\ast }{X}^{-1}K\right)\right]⩾\text{Tr}\left[\varphi {\left(K\right)}^{\ast }\varphi {\left(X\right)}^{-1}\varphi \left(K\right)\right]$holds for a wider class of positive maps that is specified here. We also comment on the connections of this inequality with various monotonicity statements that have found wide use in mathematical physics, and apply it, and a close relative, to obtain some new, definitive results. 

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3. Deformation of d = 4, $$ \mathcal{N} $$ ≥ 5 supergravities breaks nonlinear local supersymmetry

   https://doi.org/10.1007/JHEP06(2023)156  

   Kallosh, Renata; Yamada, Yusuke (June 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We studyd= 4,$$ \mathcal{N} $$ $N$≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local$$ \mathcal{H} $$ $H$-symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry. This result implies, in particular, that if$$ \mathcal{N} $$ $N$= 5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality. 

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4. $$ \mathcal{N} $$ = 2 JT supergravity and matrix models

   https://doi.org/10.1007/JHEP12(2023)003  

   Turiaci, Gustavo J.; Witten, Edward (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Generalizing previous results for$$ \mathcal{N} $$ $N$= 0 and$$ \mathcal{N} $$ $N$= 1, we analyze$$ \mathcal{N} $$ $N$= 2 JT supergravity on asymptotically AdS₂spaces with arbitrary topology and show that this theory of gravity is dual, in a holographic sense, to a certain random matrix ensemble in which supermultiplets of differentR-charge are statistically independent and each is described by its own$$ \mathcal{N} $$ $N$= 2 random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with theR-charge. In order to compare supergravity to random matrix theory, we develop an$$ \mathcal{N} $$ $N$= 2 analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case. 

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5. Measurement of branching-fraction ratios and CP asymmetries in B± → DCP±K± decays at Belle and Belle II

   https://doi.org/10.1007/JHEP05(2024)212  

   Adachi, I; Aggarwal, L; Aihara, H; Akopov, N; Aloisio, A; Anh_Ky, N; Asner, D M; Atmacan, H; Aushev, T; Aushev, V; et al (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We report results from a study ofB^±→ DK^±decays followed byDdecaying to theCP-even final stateK⁺K⁻and CP-odd final state$$ {K}_S^0{\pi}^0 $$ $K_S^0{\pi }^0$, whereDis an admixture ofD⁰and$$ {\overline{D}}^0 $$ ${\overline{D}}^0$states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angleϕ₃. The results are based on a combined analysis of the final data set of 772×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle experiment and a data set of 198×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be$$ \mathcal{A} $$ $A$_CP+= (+12.5±5.8±1.4)% and$$ \mathcal{A} $$ $A$_CP−= (−16.7±5.7±0.6)%, and the ratios of branching fractions to be$$ \mathcal{R} $$ $R$_CP+= 1.164±0.081±0.036 and$$ \mathcal{R} $$ $R$_CP−= 1.151±0.074±0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries$$ \mathcal{A} $$ $A$_CP+and$$ \mathcal{A} $$ $A$_CP−have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^°<ϕ₃< 16.5^°) or (84.5^°<ϕ₃< 95.5^°) or (163.3^°<ϕ₃< 171.5^°) and 0.321 <r_B< 0.465. 

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