We revisit the species scale in quantum gravity from the viewpoint of effective field theory (EFT). Two common parametric characterizations relate it to the breakdown of perturbative gravity and to the suppression scale of higher-derivative gravitational operators. We examine their correspondence through local threshold corrections from infinite Kaluza–Klein (KK) towers. In four dimensions, we compute the four-derivative one-loop action of minimally coupled scalar and Dirac towers with KK spectra in graviton, radion, and photon backgrounds. Feynman diagrams determine the single-mode coefficients, while analytic summation with full threshold functions tests the logarithmic coefficient inferred from renormalization-group evolution. The leading contribution scales with the effective number of KK levels, reproducing the standard species-scale relation under the stated matching assumptions, but its coefficient depends on the cutoff profile and is part of the EFT matching data. In contrast, the subleading curvature-squared thresholds contain logarithms of the KK mass gap whose spin-dependent coefficients remain stable under changes of the cutoff profile within the class studied here.

Japan

Yuri Michinobu

Kaluza–Klein Tower Thresholds and Scheme Dependence of the Species Scale

In the late 1990s, Suzuki and Yasuta proposed a compact formula that extracts the decay rate per unit volume of a false vacuum in the <italic>D</italic>-dimensional <inline-formula><tex-math id='TM0002' notation='LaTeX'>$O(N)$</tex-math></inline-formula> <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\lambda (\phi ^2)^2$</tex-math></inline-formula> theory with an unbounded potential from conventional perturbative coefficients of the vacuum energy density, i.e. vacuum bubble diagrams. The idea was to identify the imaginary part arising from the Borel integral along the discontinuity of the Borel transform with that of the vacuum energy density. While the formula works quite well for <italic>D</italic>&#160;=&#160;1, i.e. quantum mechanics, its validity remained unclear for <inline-formula><tex-math id='TM0005' notation='LaTeX'>$D\ge 2$</tex-math></inline-formula> because only the first three perturbative coefficients for&#160; <italic>D</italic>&#160;=&#160;2 were available and the result showed no sign of convergence. In the present paper, we reexamine this approach using the first seven nontrivial perturbative coefficients (up to nine loops) for&#160; <italic>D</italic>&#160;=&#160;2 and&#160; <italic>N</italic>&#160;=&#160;1 obtained by Serone, Spada, and&#160;Villadoro. Introducing two tunable parameters in the finite-order truncated Borel transform following these authors, we find that the imaginary part converges as the perturbative order increases, with the last few orders agreeing to within a few percent. In the intermediate range of the coupling constant, <inline-formula><tex-math id='TM0009' notation='LaTeX'>$3\lesssim \widetilde{g}\lesssim 8$</tex-math></inline-formula>, this approach yields an imaginary part rather close to the leading-order semiclassical approximation with the one-loop determinant; it is 10&#8211; <inline-formula><tex-math id='TM0010' notation='LaTeX'>$20\%$</tex-math></inline-formula> larger than the semiclassical result with the two-loop correction computed by Malatesta, Parisi, and Rizzo. Our result is consistent, within errors, with the continuum extrapolation of the Pad&#233;-resummed linked-cluster expansion in a quantum <inline-formula><tex-math id='TM0011' notation='LaTeX'>$\phi ^4$</tex-math></inline-formula> chain.

Hiroshi Suzuki

Quantum Tunneling from Perturbation Theory Revisited

We study the 1D generalized Dirac oscillator with a complex Morse interaction, <inline-formula><tex-math id='TM0001' notation='LaTeX'>$f(x)=D-qe^{-\alpha x}$</tex-math></inline-formula>, in the Magueijo&#8211;Smolin (MS) and Amelino-Camelia (AC) realizations of doubly special relativity (DSR). The spatial problem factorizes into supersymmetric partners. For <inline-formula><tex-math id='TM0002' notation='LaTeX'>$D\gt 0$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\mathrm{Re}\, q\gt 0$</tex-math></inline-formula>, the positive metric <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\eta =\exp (-\theta p/\hbar )$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\theta =2\arg q/\alpha$</tex-math></inline-formula>, defines, on analytic bound states, a similarity transformation <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\rho =\eta ^{1/2}$</tex-math></inline-formula> to a Hermitian Morse representative. Direct Kummer analysis on the complex ray gives the real spectrum <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\epsilon _n=D^2-(D-n\hbar \alpha )^2$</tex-math></inline-formula>, independent of the phase of <italic>q</italic>, with <inline-formula><tex-math id='TM0009' notation='LaTeX'>$0\le n\lt D/(\hbar \alpha )$</tex-math></inline-formula> following from square integrability on the whole line. We relate the Morse parameters to the DSR scale <italic>k</italic>. Both DSR equations&#160;preserve the spatial spectrum but deform energy reconstruction and spinor amplitudes. On admissible branches, <inline-formula><tex-math id='TM0011' notation='LaTeX'>$E^{\rm MS}_{n,\sigma }=\sigma \Omega _n-m^2/k$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0012' notation='LaTeX'>$E^{\rm AC}_{n,\sigma }=\sigma \Omega _n+\epsilon _n/(2k)$</tex-math></inline-formula> to first order, with <inline-formula><tex-math id='TM0013' notation='LaTeX'>$\Omega _n=\sqrt{m^2+\epsilon _n}$</tex-math></inline-formula>. On nonzero SUSY doublets, the AC generalized-eigenvalue weight is positive exactly for <inline-formula><tex-math id='TM0014' notation='LaTeX'>$\epsilon _n\lt 4k^2$</tex-math></inline-formula>. At this boundary the positive branch diverges while the negative branch remains finite, yielding a Morse excitation threshold. Quantitative use requires <inline-formula><tex-math id='TM0015' notation='LaTeX'>$|E|/k\ll 1$</tex-math></inline-formula>. The model provides an exactly solvable testbed linking pseudo-hermiticity, supersymmetry, and DSR kinematics.

Algeria

Abdelmalek Boumali

The Generalized Dirac Oscillator in Doubly Special Relativity: A Complexified Morse Interaction

We discuss the AdS/CFT correspondence from the viewpoint of gravity as a broken phase of conformal gauge symmetry. In AdS <inline-formula><tex-math id='TM0001' notation='LaTeX'>$_2$</tex-math></inline-formula>/CFT <inline-formula><tex-math id='TM0002' notation='LaTeX'>$_1$</tex-math></inline-formula>, the Schwarzian structure is related to the boundary extrinsic curvature. In AdS <inline-formula><tex-math id='TM0003' notation='LaTeX'>$_4$</tex-math></inline-formula>/CFT <inline-formula><tex-math id='TM0004' notation='LaTeX'>$_3$</tex-math></inline-formula>, the gauge-theoretic formulation of four-dimensional gravity contains a boundary-sensitive Euler sector whose descent structure leads to the Cotton tensor characterizing the three-dimensional boundary conformal geometry. At the structural and kinematical level considered here, these results suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken bulk conformal gauge symmetry.

Takeshi Fukuyama

Gauge Theory of Gravity and the AdS/CFT Correspondence

We report the results of a search for sub-GeV axion-like particles (ALPs) using pilot run data from the Electron Beam-dump Experiment at KEK Linac Switching Yard 3 (EBES). The data were collected in December 2023 with a 4 GeV positron beam and correspond to <inline-formula><tex-math id='TM0001' notation='LaTeX'>$5.7\times 10^{13}$</tex-math></inline-formula> positrons on target. In the pilot run setup, a tungsten beam dump and a single PbO calorimeter were used. We consider ALP production via the Primakoff process induced by bremsstrahlung photons in the beam dump, followed by the decay <inline-formula><tex-math id='TM0002' notation='LaTeX'>$a\rightarrow \gamma \gamma$</tex-math></inline-formula>. The background was estimated with a data-driven method, and a signal region was defined such that the expected background yield is below 0.1 events. No events were observed after unblinding. Upper limits at the 90% confidence level were derived in the ALP mass&#8211;coupling plane, extending the experimental coverage into a region of parameter space not explored by previous searches.

Takahiro Fusayasu

Tomoya Iizawa

Fumihito Ikeda

Akimasa Ishikawa

Masako Iwasaki

Hiroshi Iwase

Takahiro Kawahara

Aoi Masaki

Fusashi Miyahara

Yu Morikawa

Yuichi Okayasu

Toshiyuki Ono

Hidetoshi Otono

Yasuhito Sakaki

Takumi Seino

Yuta Shimasaki

Taikan Suehara

Yosuke Takubo

Shusaku Tsumura

Kosuke Uemura

Yifu Zhang

Search for Sub-GeV Axion-Like Particles at the EBES Pilot Run Using a 4 GeV Positron Beam at the KEK Linac

We investigate the vacuum expectation value of a complex scalar field on a 2D torus with quantized magnetic flux <italic>M</italic>. A characteristic feature of this system is the emergence of a critical area: When the area of the torus exceeds this critical value, the vacuum expectation value becomes nonvanishing. Furthermore, any nonzero vacuum expectation value necessarily exhibits nontrivial dependence on the coordinates of the torus. Employing the lowest-mode approximation, we find a single vacuum configuration for <italic>M</italic>&#160;=&#160;1, whereas two and six degenerate vacuum configurations arise for <italic>M</italic>&#160;=&#160;2 and <italic>M</italic>&#160;=&#160;3, respectively. We then analyze the symmetry properties of these vacuum configurations and determine whether they preserve or spontaneously break the symmetry of the underlying system.

Mayumi Akamatsu

Hiroki Imai

Makoto Sakamoto

Maki Takeuchi

Vacuum Structure of a Scalar Field on a Torus with Uniform Magnetic Flux

The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough elucidation. We introduce a novel probabilistic interpretation scheme for complex compositeness of resonances, in which resonances with large decay widths fall outside the domain where their internal structure can be interpreted probabilistically. Employing this scheme to analyze resonances via the effective range expansion, we demonstrate that narrow interpretable near-threshold resonances have a small composite fraction, in sharp contrast to shallow bound states below the threshold.

Tomona Kinugawa

Tetsuo Hyodo

Compositeness of Near-Threshold <italic>s</italic>-Wave Resonances

We investigate stringy constraints on moduli spaces in modular flavor models by analyzing moduli-dependent threshold corrections in heterotic string vacua. While moduli play a crucial role in determining the flavor structure of fermions predicted by modular flavor models, the parameter space in which their vacuum expectation values are allowed has not been fully explored. In this work, within the framework of perturbative heterotic string theory on toroidal orbifolds, we derive the constraints on the moduli space and study their systematic behavior. We characterize the stringy constraints in terms of the dilaton, the beta function coefficients, and the ratio between the complex-structure modulus and Kähler modulus. It is found that a large value of the modulus controlling the flavor structure, i.e. <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\tau \simeq i \infty$</tex-math></inline-formula>, is inconsistent within perturbative string theory, and the self-dual point <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\tau =i$</tex-math></inline-formula> is also disfavored in the large-volume regime of toroidal backgrounds. In addition, we discuss the phenomenological implications of these stringy constraints.

Keiya Ishiguro

Takafumi Kai

Tatsuo Kobayashi

Hajime Otsuka

Stringy Constraints on Modular Flavor Models

In this work, Bogomol’nyi–Prasad–Sommerfield (BPS) models built from the coupling of the Yang–Mills–Higgs Lagrangian to impurities are investigated. We first consider scalar impurities, which in the BPS limit generate monopoles similar to those obtained in a previously considered class of <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathrm{SU(2)}\times \mathrm{Z}_2$</tex-math></inline-formula> or <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\mathrm{SU(2)}\times \mathrm{SU(2)}$</tex-math></inline-formula> models. We then focus on the coupling to non-Abelian impurities, defined as fixed backgrounds produced by fields transforming under the adjoint representation of SU(2), with a coupling chosen to preserve half of the BPS sectors. The nature of this coupling, the ensuing Bogomol&#8217;nyi bound and BPS equations, as well as the effect of these impurities on the abelianization that leads to the emergence of a U(1) gauge group are investigated. We also verify that these impurity models can be derived as effective theories from a homogeneous <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\rm {SU(2)}\times \widetilde{\rm {SU}}(2)$</tex-math></inline-formula> Yang&#8211;Mills&#8211;Higgs parent model with a bridge field. In this interpretation, the SU(2) impurities of the effective impurity-doped theory are produced by frozen antimonopoles from the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\widetilde{\rm {SU}}(2)$</tex-math></inline-formula> sector. We study in greater detail impurities with spherical symmetry, and examine the manner in which impurity coupling changes the asymptotic behavior and range of monopole interactions. Moreover, we introduce a method that can be used to approximate solutions with the use of small perturbations around the Prasad&#8211;Sommerfield monopole. In order to exemplify the most important properties of the theory, several specific impurity models are presented, and the corresponding monopole solutions are found numerically. These solutions present novel internal structure and multiple features that would not be possible in the original theory.

Brazil

D Bazeia

M A Liao

M A Marques

Magnetic Monopoles in Yang–Mills–Higgs Theory with Impurities

We study black-hole quasinormal modes by applying the complex-scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner–Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge–Wheeler equation and then extend it to the Reissner–Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.

Shoya Ogawa

Takuya Hirose

Okuto Morikawa

Complex-Scaling Approach to Quasinormal Modes of Schwarzschild and Reissner–Nordström Black Holes