In the functional-integral formulation of Euclidean field theory, exact renormalization group (ERG) transformations are realized by functional-integral kernels. Unlike the ERG flow equations that describe infinitesimal ERG transformations, these ERG kernels explicitly depend on the global topology of the configuration space. This paper explores this topology dependence for multiply connected configuration spaces. We show that the ERG kernel is in general given by a weighted sum of kernels on its universal covering space, where the weight factors are determined by a one-dimensional representation of the fundamental group. These weight factors are shown never to be renormalized under the ERG. We also show that these factors can be interpreted as Aharonov–Bohm phases with respect to a background magnetic flux penetrating the infinite-dimensional configuration space. From this viewpoint, a normalization condition for ERG transformations corresponds to a flux-quantization condition, which is equivalent to the level-quantization condition for Wess–Zumino–Witten terms in nonlinear sigma models. Finally, we present an alternative gauge-equivalent form of the ERG flow equation that incorporates this topological information locally.

Japan

Satoshi Ohya

Taichi Tanaka

ERG Kernels on Multiply Connected Configuration Spaces

We present a momentum measurement method based on multiple Coulomb scattering in the FASER <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\nu$</tex-math></inline-formula> emulsion detector. The measurement of charged-particle momenta is essential for studying neutrino interactions in the TeV energy range in the FASER experiment. This method exploits the submicron spatial resolution and long tracking length of the FASER <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\nu$</tex-math></inline-formula> detector, enabling momentum determination from a few GeV up to a few TeV. The performance was evaluated using Geant4-based Monte Carlo simulations and validated with muon test-beam data in the momentum range 100&#8211;300 GeV. As a first probe of the method for higher-momentum muons, background muons recorded by the FASER <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\nu$</tex-math></inline-formula> detector were examined, showing reconstructed momenta consistent with expectations from their angular spread.

United States

Roshan Mammen Abraham

China

Xiaocong Ai

Switzerland

Saul Alonso Monsalve

United Kingdom

John Anders

Emma Kate Anderson

Claire Antel

Akitaka Ariga

Tomoko Ariga

Jeremy Atkinson

Germany

Florian U Bernlochner

Tobias Boeckh

Eliot Bornand

Jamie Boyd

Netherlands

Lydia Brenner

France

Angela Burger

Franck Cadoux

Roberto Cardella

David W Casper

Charlotte Cavanagh

Shiyang Chen

Xin Chen

Xing Cheng

Kohei Chinone

Dhruv Chouhan

Italy

Andrea Coccaro

Stephane Débieux

Ansh Desai

Sergey Dmitrievsky

Romania

Radu Dobre

Monica D’Onofrio

Sinead Eley

Yannick Favre

Jonathan L Feng

Carlo Alberto Fenoglio

Didier Ferrere

Max Fieg

Wissal Filali

Elena Firu

Haruhi Fujimori

Edward Galantay

Ali Garabaglu

Stephen Gibson

Sergio Gonzalez-Sevilla

Yuri Gornushkin

Israel

Yotam Granov

Jinjing Gu

Carl Gwilliam

Elie Hammou

Daiki Hayakawa

Michael Holzbock

Shih-Chieh Hsu

Zhen Hu

Giuseppe Iacobucci

Tomohiro Inada

Luca Iodice

Sune Jakobsen

Cesar Jesus-Valls

Arash Jofrehei

Hans Joos

Enrique Kajomovitz

Takumi Kanai

Hiroaki Kawahara

Alex Keyken

Felix Kling

Daniela Köck

Pantelis Kontaxakis

Jelle Koorn

Umut Kose

Peter Krack

Susanne Kuehn

Thanushan Kugathasan

Sebastian Laudage

Lorne Levinson

Botao Li

Jinfeng Liu

Yi Liu

Margaret S Lutz

Jack MacDonald

Joern Mahlstedt

Toni Mäkelä

Anna Mascellani

Lawson McCoy

Josh McFayden

Andrea Pizarro Medina

Théo Moretti

Keiko Moriyama

Toshiyuki Nakano

Laurie Nevay

Motoya Nonaka

Yuma Ohara

Ken Ohashi

Kazuaki Okui

Hidetoshi Otono

Lorenzo Paolozzi

Annabelle Parry

Pawan Pawan

Brian Petersen

Titi Preda

Markus Prim

Junkai Qin

Momentum Measurement of Charged Particles in FASER’s Emulsion Detector at the LHC

In order to ensure measurement of the integrated luminosity with a relative precision of <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathrm{10^{-4}}$</tex-math></inline-formula> at the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\mathrm{Z^{0}}$</tex-math></inline-formula> pole at the Circular Electron Positron Collider (CEPC), numerous systematic effects have to be quantified and, if possible, corrected for. Here we discuss the collective impact of electromagnetic bunch fields on the initial-state electrons and positrons (EMD1) as well as on the Bhabha scattering final states (EMD2). Both effects change the four-momenta of the final-state particles, leading to modification of the Bhabha count in the luminometer. These effects are quantified in a simulation, together with their stability with respect to beam parameter variations. Possible correction methods based on experimental measurements with the CEPC detector are discussed on a conceptual level.

Serbia

Ivan Smiljanić

Ivanka Božović

Ivana Vidaković

Nataša Vukašinović

Goran Kačarević

Electromagnetic Deflection Effects in the Integrated Luminosity Measurement at the CEPC

With the discovery of nonzero <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\theta _{13}$</tex-math></inline-formula> and a near-maximal value of the Dirac CP phase as reflected from the measurements of the T2K and NO <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\nu$</tex-math></inline-formula>A experiments, the significance of <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry becomes more prominent. In this work, we study the renormalization group (RG) running effects on neutrino parameters as a perturbation to <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry. Assuming the symmetry to be exact at the seesaw scale, we account the deviations of the parameters at the electroweak scale due to RG running. We solve numerically a set of 19 one-loop RG equations in total, including those of neutrino mixing parameters, mass eigenvalues, and gauge and Yukawa couplings, using a top-down approach. We aim to examine the consistency of the low-energy solutions at the EW scale with the observational data. Working in the Minimal Supersymmetric Standard Model framework, we choose three benchmark values at <inline-formula><tex-math id='TM0006' notation='LaTeX'>$1\ \text{TeV},\ 7\ \text{TeV}$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0007' notation='LaTeX'>$14\ \text{TeV}$</tex-math></inline-formula> for the supersymmetry breaking scale intermediate between the seesaw scale and EW scale. This requires a two-step running procedure to solve the RG equations and it also allows us to study the impact of variation of the supersymmetry breaking scale on the running effects. Our numerical results indicate that the deviations from <inline-formula><tex-math id='TM0008' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry induced by RG running remain compatible with the current <inline-formula><tex-math id='TM0009' notation='LaTeX'>$3\sigma$</tex-math></inline-formula> global oscillation data.

India

Chandan Kumar Borah

Chandan Duarah

Perturbations to <italic>&#956;-&#964;</italic> Reflection Symmetry Due to Renormalization Group Running Effects

We propose gauge-invariant criteria for center-vortex condensation and monopole condensation using the <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathbb {Z}_N^{[1]}$</tex-math></inline-formula>-symmetry twisted partition functions: the torus twisted partition function characterizes the center-vortex condensation, and the lens-space twisted partition function characterizes the monopole condensation. To justify our proposal, we study how these twisted partition functions behave in the adjoint Higgs phase and show that their leading nontrivial contributions come from the center vortex and monopole, respectively. Using the techniques of topological field theories, we uncover the relationship between the center-vortex and monopole condensations, and, in particular, we prove that the gapped phase with the center-vortex condensation necessarily shows the monopole condensation, too. We then study a center-vortex model with monopoles as an illustrative example, and the higher-charge monopole condensation gives an example of symmetry fractionalization, which goes beyond the conventional Wilson&#8211;&#8217;t Hooft classification.

Yui Hayashi

Yuya Tanizaki

Monopoles, Center Vortices, Confinement in (3+1)D, and the Lens-Space Twisted Partition Function

We introduce the <italic>latent entropy</italic> ( <italic>L</italic>-entropy) as a novel measure to characterize the genuine multipartite entanglement in quantum systems. Our measure leverages the upper bound of reflected entropy and its maximal values attained by 2-uniform states for <italic>n</italic>-party ( <inline-formula><tex-math id='TM0002' notation='LaTeX'>$n= 4,5$</tex-math></inline-formula>) and by the <italic>GHZ</italic> state for 3-party quantum systems. We demonstrate that the measure is a nonnegative, local unitary invariant function that vanishes for separable states. We then analyze its interesting characteristics in spin chain models and the Sachdev&#8211;Ye&#8211;Kitaev (SYK) model. Subsequently, we explore its implications for holography by deriving a Page-like curve for the <italic>L</italic>-entropy in the conformal field theory (CFT) dual to a multiboundary wormhole model. Furthermore, we examine the behavior of <italic>L</italic>-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for&#160; <inline-formula><tex-math id='TM0003' notation='LaTeX'>$n =5$</tex-math></inline-formula>, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multiboundary wormhole geometries. Extending to finite-temperature systems, we introduce the multipartite thermal pure quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating the state-dependent construction of the MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multicopy SYK model and examine its multipartite entanglement structure.

South Korea

Jaydeep Kumar Basak

Vinay Malvimat

Junggi Yoon

A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes

In this work, we present a new construction of black hole solutions in noncommutative (NC) gauge theory by applying the Seiberg–Witten map directly to interaction potentials before solving Einstein’s equations. This approach provides a dynamical effect of space-time noncommutativity that preserves gauge covariance. We obtain both NC Schwarzschild and charged Reissner–Nordström-like black hole solutions, showing that the charged sector exhibits a novel branch dependence between attractive and repulsive electric interactions absent in the commutative limit. We analyze the geometrical properties, energy conditions, and thermodynamic properties of these space-times. Our results reveal that noncommutativity eliminates the temperature divergence at the final evaporation stage, inducing a second-order phase transition, or a Hawking–Page-like phase transition in the presence of pressure. Additionally, linear response analysis indicates high sensitivity to the NC parameter for small black holes. Finally, quantum tunneling investigations for both thermal and nonthermal radiation demonstrate that the NC deformation suppresses the particle-number density and weakens correlations between successive emissions, acting as a barrier to particle escape, and supports the formation of a cold finite remnant. From a cosmological standpoint, since these stable remnants possess a fixed Planck-scale mass ( <inline-formula><tex-math id='TM0001' notation='LaTeX'>$M^{\text{min}}\simeq 2.73 M_{P}$</tex-math></inline-formula>), they provide a dynamically generated, purely gravitational cold dark matter candidate that aligns with dark universe phenomenology while simultaneously resolving the black hole information loss paradox.

Algeria

Abdellah Touati

New Construction of Black Hole Solutions in Noncommutative Geometry and Their Thermodynamic Properties

Recent claims have suggested the absence of CP violation in theories with a <italic>&#952;</italic>-vacuum structure, particularly in quantum chromodynamics. We highlight several key points, from a perspective that is not widely discussed in the literature, which clarify why such conclusions are incorrect. In particular, an open boundary in a finite-volume theory must be accompanied by boundary degrees of freedom, the edge modes, in order to preserve large gauge invariance and faithfully capture the topological features of the theory. In the infinite-volume limit, these edge states become nondynamical, leaving the standard <italic>&#952;</italic>-vacuum structure intact, irrespective of whether this limit is taken before or after summing over topological sectors. Consequently, the <italic>&#952;</italic>-vacuum structure does give rise to observable CP violation once the theory is consistently quantized.

Australia

Archil Kobakhidze

On the <italic>&#952;</italic>-Vacua and CP Violation

In this paper, we study the quasinormal modes (QNMs) of a charged black hole in the presence of both quintessence and a cloud of strings using the Padé-averaged higher-order Wentzel–Kramers–Brillouin approximation method. We investigate the effect of the quintessence parameter <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\alpha$</tex-math></inline-formula> and the cloud of strings parameter <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\lambda$</tex-math></inline-formula> on stability as well as on the oscillation frequency of perturbations. The validity of Hod&#8217;s conjecture, which relates quasinormal frequencies to the black hole temperature, is tested throughout the physically allowed parameter space. Our results show that both the effective potential and the decay rate of perturbations depend on the values of <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\alpha$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\lambda ,$</tex-math></inline-formula> leading to either enhancement or suppression of the conditions required to satisfy Hod&#8217;s bound. Furthermore, we discuss how these parameters modify the black hole shadow and the corresponding energy emission rate, proving correlations with observable signatures. Finally, we establish the connection with the Swampland distance conjecture by expressing the Hawking temperature in terms of the scalar field excursion. Our analysis leads to a modified Hod bound and identifies a region of parameter space in which both the modified Hod bound and the Swampland constraints are simultaneously satisfied, ensuring consistency between black hole thermodynamics, observational properties, and quantum gravity constraints.

Morocco

S Saoud

M A Rbah

R Sammani

E H Saidi

R Ahl Laamara

A Swampland-Modified Hod Bound for Charged Black Holes with Exotic Matter

Pole skipping is a universal property of Green’s functions at the strong coupling found in the AdS/CFT duality. There is a conventional formalism of pole skipping, but it relies on the existence of a “master variable.” Namely, it is applicable to a system with a single field. We propose an alternative formalism that does not rely on a master variable. As an example, we study the pole skipping of holographic superfluids. A “hydrodynamic” pole such as the diffusion pole is usually regarded as a pole-skipping point. But we point out that not all hydrodynamic poles are pole-skipping points because their residues may not vanish.

Makoto Natsuume

Takashi Okamura

Pole Skipping Without a Master Variable and Holographic Superfluids