Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step toward the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four–dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 nonisomorphic Manin triples plus their duals.

Czechia

Ladislav Hlavatý

Petr Novotný

Ivo Petr

Classification of Standard Manin Triples in Dimension 4+4

We study time-reversal symmetry in <inline-formula><tex-math id='TM0001' notation='LaTeX'>$(2+1)$</tex-math></inline-formula>D abelian bosonic topological phases. Time-reversal anomalies in such systems are classified by <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\mathbb {Z}_2 \times \mathbb {Z}_2$</tex-math></inline-formula> symmetry-protected topological (SPT) phases in <inline-formula><tex-math id='TM0003' notation='LaTeX'>$(3+1)$</tex-math></inline-formula>D, and can be diagnosed via partition functions on manifolds such as <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\mathbb {RP}^4$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\mathbb {CP}^2$</tex-math></inline-formula>. These partition functions are related by the anomaly formula <inline-formula><tex-math id='TM0006' notation='LaTeX'>$Z(\mathbb {RP}^4)\, Z(\mathbb {CP}^2) = \theta _{\mathcal {M}}$</tex-math></inline-formula>, where <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\theta _\mathcal {M}$</tex-math></inline-formula> is the Dehn twist phase associated with the crosscap state. Meanwhile, the existence of gapped boundaries is constrained by so-called <italic>higher central charges <inline-formula><tex-math id='TM0008' notation='LaTeX'>$\xi _n$</tex-math></inline-formula></italic>, which serve as computable invariants encoding obstruction data. Motivated by the known relation <inline-formula><tex-math id='TM0009' notation='LaTeX'>$Z(\mathbb {CP}^2) = \xi _1$</tex-math></inline-formula>, we propose a generalization of the anomaly formula that involves both the higher central charges <inline-formula><tex-math id='TM0010' notation='LaTeX'>$\xi _n$</tex-math></inline-formula> and a new time-reversal invariant <inline-formula><tex-math id='TM0011' notation='LaTeX'>$\eta _n$</tex-math></inline-formula>. Introducing a distinguished subset <inline-formula><tex-math id='TM0012' notation='LaTeX'>$\mathcal {M}^n \subset \mathcal {A}$</tex-math></inline-formula> of anyons, we establish the relation <inline-formula><tex-math id='TM0013' notation='LaTeX'>$\eta _n \cdot \xi _n = \frac{\sum _{a \in \mathcal {M}^n} \theta (a)^n}{\left| \sum _{a \in \mathcal {M}^n} \theta (a)^n \right|},$</tex-math></inline-formula>which generalizes the known anomaly formula. We analyze the algebraic structure of <inline-formula><tex-math id='TM0014' notation='LaTeX'>$\mathcal {M}^n$</tex-math></inline-formula>, derive consistency relations it satisfies, and clarify its connection to the original anomaly formula.

Japan

Ippo Orii

Generalization of Anomaly Formula for Time-Reversal Symmetry in (2+1)D Abelian Bosonic Topological Quantum Field Theories

The muon’s magnetic moment is a fundamental quantity in particle physics and the observed deviation of its value from the prediction of quantum electrodynamics motivated investigations beyond the Standard Model (SM). In this study, we utilize the effective coupling of right-handed sterile neutrinos with SM gauge bosons to calculate the muon anomalous magnetic moment ( <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\boldsymbol{\mu }$</tex-math></inline-formula>AMM) at one-loop level. The contribution of the sterile neutrino interactions on the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\boldsymbol{\mu }$</tex-math></inline-formula>AMM is evaluated by including both standard and nonstandard neutrino interactions. Our analysis shows that the standard sterile neutrino interactions give a negligible contribution to <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\Delta a_{\boldsymbol{\mu }}$</tex-math></inline-formula> while the nonstandard neutrino interactions can play a significant role in explaining the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$(g-2)_{\boldsymbol{\mu }}$</tex-math></inline-formula> anomaly. In the context of the nonstandard neutrino interaction, our calculation shows that a Dirac mass scale <inline-formula><tex-math id='TM0005' notation='LaTeX'>$M_\mathrm D\approx 100\, \text{GeV}$</tex-math></inline-formula> could explain the muon anomaly if the right-handed sterile neutrino&#8217;s coupling with SM particles is about <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\mathcal {G}_R\approx 10^{-3}$</tex-math></inline-formula>. Furthermore, we use the observed discrepancy in the muon anomalous magnetic moment to impose constraints on the model parameters. We present the allowed parameter space, consistent with the experimental data on <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\Delta a_{{\boldsymbol{\mu }}}^{\mathrm{ SN}}$</tex-math></inline-formula>, and discuss the percentage of the <inline-formula><tex-math id='TM0008' notation='LaTeX'>${\boldsymbol{\mu }}$</tex-math></inline-formula> anomaly compensation in terms of the coupling constant <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\mathcal {G}_R$</tex-math></inline-formula>.

France

Iman Motie

Iran

Mahdi Sadegh

S Mahmoudi

Jafar Khodagholizadeh

Alain Blanchard

Italy

China

She-Sheng Xue

Muon Anomalous Magnetic Moment and Right-Handed Sterile Neutrino

The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated <inline-formula><tex-math id='TM0001' notation='LaTeX'>$J_1$</tex-math></inline-formula>- <inline-formula><tex-math id='TM0002' notation='LaTeX'>$J_2$</tex-math></inline-formula> Ising model on the square lattice. Here <inline-formula><tex-math id='TM0003' notation='LaTeX'>$J_1 &lt; 0$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0004' notation='LaTeX'>$J_2 &gt; 0$</tex-math></inline-formula> are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of <inline-formula><tex-math id='TM0005' notation='LaTeX'>$g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7$</tex-math></inline-formula> and employ the resulting CNN to study the phase transition of <inline-formula><tex-math id='TM0006' notation='LaTeX'>$g = 0.8$</tex-math></inline-formula>. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature <inline-formula><tex-math id='TM0007' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0008' notation='LaTeX'>$g=0.7$</tex-math></inline-formula>, are needed to accurately determine the <inline-formula><tex-math id='TM0009' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0010' notation='LaTeX'>$g=0.8$</tex-math></inline-formula>. However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the <inline-formula><tex-math id='TM0011' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0012' notation='LaTeX'>$g=0.7$</tex-math></inline-formula>. Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the <inline-formula><tex-math id='TM0013' notation='LaTeX'>$T_c$</tex-math></inline-formula> of <inline-formula><tex-math id='TM0014' notation='LaTeX'>$g=0.8$</tex-math></inline-formula> accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.

Taiwan

Shang-Wei Li

Yuan-Heng Tseng

Ming-Che Hsieh

Fu-Jiun Jiang

Minimal Training Set for Training a Successful CNN: A Case Study of the Frustrated <italic>J</italic> <sub>1</sub>- <italic>J</italic> <sub>2</sub> Ising Model on the Square Lattice

Exploring the mass modifications of <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\phi$</tex-math></inline-formula> mesons in nuclei provides insights into the nature of strongly interacting matter. Specifically, <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\phi$</tex-math></inline-formula> meson mass shifts can be related to the in-medium modification of the strange quark condensate. Therefore, the partial restoration of chiral symmetry can be studied by observing the mass shifts through the decay channels <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\phi \rightarrow e^+e^-$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\phi \rightarrow K^+K^-$</tex-math></inline-formula>. In this paper, we examine the possibility of observing the <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\phi$</tex-math></inline-formula> meson mass modifications of the <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\phi$</tex-math></inline-formula> mesons in 30 GeV proton&#8211;nucleus (C, Cu, Pb) collisions, to be studied at the J-PARC E88 experiment, through the kaonic decay channel, with the off-shell Budapest Boltzmann&#8211;Uehling&#8211;Uhlenbeck transport model. By applying different mean fields to the kaons, we examine their effects on the invariant mass spectra. Our simulations suggest that, although different mean fields for the kaons do affect the spectrum, there is a common observable effect primarily driven by the <inline-formula><tex-math id='TM0008' notation='LaTeX'>$\phi$</tex-math></inline-formula> mass shift. However, due to the threshold associated with the two kaons, the signal that we observe is quite different from the one expected in dilepton spectra. Therefore, to meaningfully constrain the mass shift, it will be useful to include both kaon and dilepton channels in the analysis of the experimental data.

South Korea

Gábor Balassa

Kazuya Aoki

Philipp Gubler

Su Houng Lee

Hiroyuki Sako

Hungary

György Wolf

Studying the In-Medium φ Meson Spectrum Through Kaons in Proton–Nucleus Reactions

The Gubser–Rocha model is a holographic model that shows the linear dependence of the entropy density on the temperature. The model can be extended to possess S-duality by introducing an axio-dilaton field. With an appropriate choice of the boundary action, both models exhibit a continuous phase transition in the neutral limit. In this paper, we investigate several aspects of this phase transition. First, we show that the critical exponents of the phase transition match those of the mean-field percolation theory. Next, we analyze the dynamical stability, and the emergence of the Nambu–Goldstone modes by analyzing the quasinormal modes of the perturbation fields. The dynamical stability is consistent with the thermodynamic stability. In addition, we find that there is an emergent Nambu–Goldstone mode in the broken phase of the S-type model.

Shuta Ishigaki

Dynamical Stability and Critical Exponents of the Neutral (S-Type) Gubser–Rocha Model with Momentum Dissipation

Determining the solvability of a given quantum mechanical system is generally challenging. We discuss that the numerical bootstrap method can help us to solve this question in 1D quantum mechanics. We show that the bootstrap method can derive exact energy eigenvalues in systems with shape invariance, which is a sufficient condition for solvability and which many solvable systems satisfy. The information of the annihilation operators is also obtained naturally, and thus the bootstrap method tells us why the system is solvable. We numerically demonstrate this explicitly for shape-invariant potentials: harmonic oscillators, Morse potentials, Rosen–Morse potentials, and hyperbolic Scarf potentials. Therefore, the numerical bootstrap method can determine the solvability of a given unknown system if it satisfies shape invariance.

Yu Aikawa

Takeshi Morita

Bootstrapping Shape Invariance: Numerical Bootstrap as a Detector of Solvable Systems

The stochastic dynamics of a scalar field in de Sitter space-time can be regarded as a nonperturbative diffusion process, for which exact distribution and correlation functions are constructed by utilizing the correspondence between diffusion and Schrödinger equations. The Krein–Adler transformation of the quantum harmonic oscillator deletes several pairs of the energy levels to define anharmonic oscillators that we dub quantum deficient oscillators, based on which this article constructs a new class of exact solutions in stochastic inflation. In addition to the simplest single-well model, an exactly solvable double-well model is also presented. The results are further extended to exactly solvable models with multiple wells, allowing analytical studies on various cosmological phenomenologies.

Yuta Nasuda

Koki Tokeshi

Yuki Watanabe

Scalar Field Stochastic Dynamics in de Sitter Space-time from Exact Solutions of Quantum Deficient Oscillators

We investigate the properties of pseudoscalar <italic>D</italic> and vector <inline-formula><tex-math id='TM0004' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons in an isospin asymmetric nuclear medium using a hybrid approach that integrates the light-front quark model with the chiral SU(3) quark mean-field model. The influence of the isospin asymmetric nuclear medium is examined by utilizing the in-medium quark masses derived from the chiral SU(3) quark mean-field model as an input in the light-front quark model to study the medium modification of <italic>D</italic> mesons. We examine the impact of isospin asymmetry and baryon density at zero and finite temperature on the effective masses, weak decay constants, and distribution amplitudes of the pseudoscalar mesons <inline-formula><tex-math id='TM0006' notation='LaTeX'>$D^0$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0007' notation='LaTeX'>$D^+$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0008' notation='LaTeX'>$D_s$</tex-math></inline-formula>, and the vector mesons <inline-formula><tex-math id='TM0009' notation='LaTeX'>$D^{0*}$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0010' notation='LaTeX'>$D^{+*}$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0011' notation='LaTeX'>$D_s^{*}$</tex-math></inline-formula>. Our results indicate significant medium-induced changes for pseudoscalar <italic>D</italic> and vector <inline-formula><tex-math id='TM0013' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons with <inline-formula><tex-math id='TM0014' notation='LaTeX'>$u/d$</tex-math></inline-formula> as one of their constituent quarks, while a comparatively reduced effect is observed for mesons containing a strange quark. In contrast to temperature and isospin asymmetry, changes in the baryon density of the nuclear medium have a larger effect on different properties of <italic>D</italic> and <inline-formula><tex-math id='TM0016' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons.

India

Anshu Gautam

Dhananjay Singh

Navpreet Kaur

Satyajit Puhan

Suneel Dutt

Harleen Dahiya

Arvind Kumar

<italic>D</italic> and <italic>D*</italic> Mesons in an Isospin Asymmetric Nuclear Medium

We show that Earth’s natural environment can serve as a powerful probe for ultralight axion dark matter. In the presence of global geomagnetic fields, axions with masses ranging from <inline-formula><tex-math id='TM0001' notation='LaTeX'>$10^{-15}$</tex-math></inline-formula>&#8201;eV&#8211; <inline-formula><tex-math id='TM0002' notation='LaTeX'>$10^{-13}$</tex-math></inline-formula>&#8201;eV induce electromagnetic waves in the (sub-) extremely low-frequency band (0.3&#8211;30 Hz) through axion&#8211;photon coupling. We predict the amplitude of induced magnetic fields in the Earth&#8211;ionosphere cavity, taking the finite conductivity of the atmosphere into account. This allows us to constrain the axion&#8211;photon coupling parameter, <inline-formula><tex-math id='TM0003' notation='LaTeX'>$g_{\rm a\gamma }$</tex-math></inline-formula>, from the long-term monitoring data of the low-frequency magnetic fields, resulting in a significant improvement from the previous constraints down to <inline-formula><tex-math id='TM0004' notation='LaTeX'>$g_{\rm a\gamma }\lesssim 4\times 10^{-13}\, {\rm GeV}^{-1}$</tex-math></inline-formula> for axion mass <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\sim 3 \times 10^{-14}\, \rm {eV}$</tex-math></inline-formula>.

Atsushi Taruya

Atsushi Nishizawa

Yoshiaki Himemoto

Hunting Axion Dark Matter Signatures in Low-Frequency Terrestrial Magnetic Fields