Shao-Feng Ge, Chui-Fan Kong, Manfred Lindner, João Paulo Pinheiro
The first results from the JUNO reactor neutrino oscillation experiment improve our knowledge of neutrino masses and mixing parameters, especially the solar angle θs ≡ θ12 and the solar mass squared difference ( Delta {m}_s^2equiv Delta {m}_{21}^2 ). We discuss the implications of these results on neutrinoless double beta decay by itself and in combination with the global fit of neutrino oscillation experiments, the JUNO first data, and cosmological constraints on the neutrino mass sum. For the effective mass ⟨mee⟩, the uncertainties in its lower limits for both mass orderings and upper limits for the normal ordering are largely reduced. Since the cosmological CMB and DESI BAO data put a stringent constraint on the neutrino mass scale, we also show how the probability distribution of both the real and imaginary parts of the effective mass ⟨mee⟩ on the complex plane is affected. Especially, the funnel region with |⟨mee⟩| ≲ 1 meV receives larger chance to happen. Correspondingly, the chance of determining the two Majorana CP phases simultaneously in this region also increases with reduced uncertainty.
{"title":"Neutrinoless double beta decay in light of JUNO first data","authors":"Shao-Feng Ge, Chui-Fan Kong, Manfred Lindner, João Paulo Pinheiro","doi":"10.1007/JHEP03(2026)105","DOIUrl":"10.1007/JHEP03(2026)105","url":null,"abstract":"<p>The first results from the JUNO reactor neutrino oscillation experiment improve our knowledge of neutrino masses and mixing parameters, especially the solar angle <i>θ</i><sub><i>s</i></sub> ≡ <i>θ</i><sub>12</sub> and the solar mass squared difference <span>( Delta {m}_s^2equiv Delta {m}_{21}^2 )</span>. We discuss the implications of these results on neutrinoless double beta decay by itself and in combination with the global fit of neutrino oscillation experiments, the JUNO first data, and cosmological constraints on the neutrino mass sum. For the effective mass ⟨<i>m</i><sub><i>ee</i></sub>⟩, the uncertainties in its lower limits for both mass orderings and upper limits for the normal ordering are largely reduced. Since the cosmological CMB and DESI BAO data put a stringent constraint on the neutrino mass scale, we also show how the probability distribution of both the real and imaginary parts of the effective mass ⟨<i>m</i><sub><i>ee</i></sub>⟩ on the complex plane is affected. Especially, the funnel region with |⟨<i>m</i><sub><i>ee</i></sub>⟩| ≲ 1 meV receives larger chance to happen. Correspondingly, the chance of determining the two Majorana CP phases simultaneously in this region also increases with reduced uncertainty.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)105.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qianteng Zhu, Gert Aarts, Wei Wang, Kai Zhou, Lingxiao Wang
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.
{"title":"Physics-conditioned diffusion models for lattice gauge theory","authors":"Qianteng Zhu, Gert Aarts, Wei Wang, Kai Zhou, Lingxiao Wang","doi":"10.1007/JHEP03(2026)111","DOIUrl":"10.1007/JHEP03(2026)111","url":null,"abstract":"<p>We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)111.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sub-GeV dark matter (DM) with s-channel resonant self-scattering provides a promising framework for addressing small-scale structure problems. However, models that also account for the observed relic abundance through the same resonance are strongly constrained by current γ-ray observations, since the associated signals are significantly enhanced. To overcome this limitation, we propose a framework in which the relic abundance and self-scattering are governed independently by two distinct mediators. As a concrete realization, we present a singlet scalar DM model in which self-scattering is mediated by a vector boson associated with a gauged baryon number, while the relic density is determined by forbidden annihilation into dark Higgs bosons that generate the gauge boson mass. By imposing cosmological, experimental, and theoretical constraints, We identify viable parameter regions that reproduce the observed relic density, alleviate small-scale problems, and remain consistent with current bounds. Notably, the model predicts multiple distinctive MeV γ-ray signals, a significant fraction of which will be testable with next-generation MeV γ-ray telescopes, including the Compton Spectrometer and Imager (COSI).
{"title":"Self-interacting sub-GeV dark matter with strong MeV gamma-ray","authors":"Yu Watanabe","doi":"10.1007/JHEP03(2026)104","DOIUrl":"10.1007/JHEP03(2026)104","url":null,"abstract":"<p>Sub-GeV dark matter (DM) with <i>s</i>-channel resonant self-scattering provides a promising framework for addressing small-scale structure problems. However, models that also account for the observed relic abundance through the same resonance are strongly constrained by current <i>γ</i>-ray observations, since the associated signals are significantly enhanced. To overcome this limitation, we propose a framework in which the relic abundance and self-scattering are governed independently by two distinct mediators. As a concrete realization, we present a singlet scalar DM model in which self-scattering is mediated by a vector boson associated with a gauged baryon number, while the relic density is determined by forbidden annihilation into dark Higgs bosons that generate the gauge boson mass. By imposing cosmological, experimental, and theoretical constraints, We identify viable parameter regions that reproduce the observed relic density, alleviate small-scale problems, and remain consistent with current bounds. Notably, the model predicts multiple distinctive MeV <i>γ</i>-ray signals, a significant fraction of which will be testable with next-generation MeV <i>γ</i>-ray telescopes, including the Compton Spectrometer and Imager (COSI).</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)104.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Leonardo Bonino, Thomas Gehrmann, Markus Löchner, Kay Schönwald, Giovanni Stagnitto
The semi-inclusive production of identified hadrons in deeply inelastic lepton scattering on polarized nucleons allows to probe the spin structure of the nucleon target in a more detailed level than through fully inclusive processes. We compute the NNLO QCD corrections to longitudinally polarized semi-inclusive deep inelastic processes mediated by electroweak neutral and charged currents. We present the first calculation of polarized electroweak structure functions in the Larin scheme up to NNLO. Additionally, we reformulate the finite scheme transformation to the ( overline{textrm{MS}} ) scheme in a quark flavour basis and identify issues in its assignment to partonic channels in previous calculations. Using our results we perform a detailed phenomenological study of polarized cross sections and of single and double spin asymmetries. We observe large electroweak effects, which need to be included in precision studies of polarized observables.
{"title":"Polarized neutral and charged current semi-inclusive deep-inelastic scattering at NNLO in QCD","authors":"Leonardo Bonino, Thomas Gehrmann, Markus Löchner, Kay Schönwald, Giovanni Stagnitto","doi":"10.1007/JHEP03(2026)109","DOIUrl":"10.1007/JHEP03(2026)109","url":null,"abstract":"<p>The semi-inclusive production of identified hadrons in deeply inelastic lepton scattering on polarized nucleons allows to probe the spin structure of the nucleon target in a more detailed level than through fully inclusive processes. We compute the NNLO QCD corrections to longitudinally polarized semi-inclusive deep inelastic processes mediated by electroweak neutral and charged currents. We present the first calculation of polarized electroweak structure functions in the Larin scheme up to NNLO. Additionally, we reformulate the finite scheme transformation to the <span>( overline{textrm{MS}} )</span> scheme in a quark flavour basis and identify issues in its assignment to partonic channels in previous calculations. Using our results we perform a detailed phenomenological study of polarized cross sections and of single and double spin asymmetries. We observe large electroweak effects, which need to be included in precision studies of polarized observables.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)109.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The laser of an intense electromagnetic field promotes the studies of strong-field particle physics in high-intensity frontier. Particle accelerator facilities in the world produce high-quality muon and proton beams. In this work, we propose the nonlinear Compton scattering to light dark particles through the collision between intense laser pulse and muon or proton beam. We take light dark photon and axion-like particle as illustrative dark particles. The cross sections of relevant nonlinear Compton scattering to dark photon or axion-like particle are calculated. We also analyze the background processes with missing neutrinos. The prospective sensitivity shows that the laser-induced process provides a complementary and competitive search of new invisible particles lighter than about 1 MeV.
{"title":"Production of light dark particles from nonlinear Compton scattering between intense laser and muon or proton beam","authors":"Tong Li, Kai Ma, Man Yuan","doi":"10.1007/JHEP03(2026)107","DOIUrl":"10.1007/JHEP03(2026)107","url":null,"abstract":"<p>The laser of an intense electromagnetic field promotes the studies of strong-field particle physics in high-intensity frontier. Particle accelerator facilities in the world produce high-quality muon and proton beams. In this work, we propose the nonlinear Compton scattering to light dark particles through the collision between intense laser pulse and muon or proton beam. We take light dark photon and axion-like particle as illustrative dark particles. The cross sections of relevant nonlinear Compton scattering to dark photon or axion-like particle are calculated. We also analyze the background processes with missing neutrinos. The prospective sensitivity shows that the laser-induced process provides a complementary and competitive search of new invisible particles lighter than about 1 MeV.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)107.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose boundary terms for the action of the NS sector of supergravity on M3 × S3 × T4 spacetimes — where M3 is an AdS3 or a linear dilaton background — that render the Brown-York stress tensor and the on-shell action finite. For AdS3 backgrounds, we show that the on-shell action yields a free energy with chemical potentials determined by the B-field. TsT (T-duality + shift + T-duality) transformations of these backgrounds generate classes of linear dilaton backgrounds distinguished by their boundary conditions. Among them, there is one class of backgrounds that reproduces features of the single-trace ( Toverline{T} ) deformation. These backgrounds have additional chemical potentials that can be turned off by large gauge transformations of the B-field. We show that the Brown-York stress tensor of these backgrounds reproduces the energies and the trace flow equation of ( Toverline{T} )-deformed CFTs. We also show that the on-shell action matches the ( Toverline{T} ) partition function and discuss the interpretation of these results.
{"title":"The on-shell action of supergravity & the B-side of TsT and single-trace ( Toverline{T} )","authors":"Luis Apolo","doi":"10.1007/JHEP03(2026)098","DOIUrl":"10.1007/JHEP03(2026)098","url":null,"abstract":"<p>We propose boundary terms for the action of the NS sector of supergravity on <i>M</i><sub>3</sub> × <i>S</i><sup>3</sup> × <i>T</i><sup>4</sup> spacetimes — where <i>M</i><sub>3</sub> is an AdS<sub>3</sub> or a linear dilaton background — that render the Brown-York stress tensor and the on-shell action finite. For AdS<sub>3</sub> backgrounds, we show that the on-shell action yields a free energy with chemical potentials determined by the <i>B</i>-field. TsT (T-duality + shift + T-duality) transformations of these backgrounds generate classes of linear dilaton backgrounds distinguished by their boundary conditions. Among them, there is one class of backgrounds that reproduces features of the single-trace <span>( Toverline{T} )</span> deformation. These backgrounds have additional chemical potentials that can be turned off by large gauge transformations of the <i>B</i>-field. We show that the Brown-York stress tensor of these backgrounds reproduces the energies and the trace flow equation of <span>( Toverline{T} )</span>-deformed CFTs. We also show that the on-shell action matches the <span>( Toverline{T} )</span> partition function and discuss the interpretation of these results.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)098.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large N ungauged one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states that signal nonequilibrium phase transitions. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.
{"title":"Nonequilibrium phase transitions in Large N matrix quantum mechanics","authors":"Minjae Cho","doi":"10.1007/JHEP03(2026)092","DOIUrl":"10.1007/JHEP03(2026)092","url":null,"abstract":"<p>It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large <i>N</i> ungauged one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states that signal nonequilibrium phase transitions. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)092.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xin-Xiang Ju, Bo-Hao Liu, Ya-Wen Sun, Bo-Yu Xu, Yang Zhao
We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range entanglement and hyperbolic modifications that suppress them. We utilize various multipartite entanglement measures/signals to analyze the multipartite entanglement structures. These measures/signals are combinations of entanglement entropy, multi-entropy, entanglement wedge cross sections (EWCS) and multi-EWCS. Our results reveal that in the extremal limits of these two geometric modifications, the multipartite entanglement structures exhibit starkly contrasting behaviors: various measures saturate either their theoretical upper or lower bounds in the respective geometries. This demonstrates that IR deformations provide a practical holographic framework for realizing extremal entanglement regimes. Moreover, it serves as an effective tool for studying quantum marginal problems in holography. Finally, by observing how different measures respond to these engineered geometries, we gain clarifying insights into the specific types of multipartite entanglement that each measure/signal is particularly sensitive to.
{"title":"Holographic multipartite entanglement structures in IR modified geometries","authors":"Xin-Xiang Ju, Bo-Hao Liu, Ya-Wen Sun, Bo-Yu Xu, Yang Zhao","doi":"10.1007/JHEP03(2026)095","DOIUrl":"10.1007/JHEP03(2026)095","url":null,"abstract":"<p>We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range entanglement and hyperbolic modifications that suppress them. We utilize various multipartite entanglement measures/signals to analyze the multipartite entanglement structures. These measures/signals are combinations of entanglement entropy, multi-entropy, entanglement wedge cross sections (EWCS) and multi-EWCS. Our results reveal that in the extremal limits of these two geometric modifications, the multipartite entanglement structures exhibit starkly contrasting behaviors: various measures saturate either their theoretical upper or lower bounds in the respective geometries. This demonstrates that IR deformations provide a practical holographic framework for realizing extremal entanglement regimes. Moreover, it serves as an effective tool for studying quantum marginal problems in holography. Finally, by observing how different measures respond to these engineered geometries, we gain clarifying insights into the specific types of multipartite entanglement that each measure/signal is particularly sensitive to.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)095.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use the results of our companion paper [J. Phys. A58 (2025) 495201], which explores the equivariant generalization of the constant-map contribution in topological string theory on toric Calabi-Yau manifolds X, to establish a holographic correspondence with M2-brane partition functions. We rigorously test this conjecture within the perturbative regime, incorporating all finite N corrections on the field theory side. Our approach involves additional key details, such as incorporating effective 4d higher-derivative supergravity corrections to introduce refinement. A central result is the derivation of the Airy function representation for the squashed S3 partition function of the field theory, for an arbitrary squashing parameter. We demonstrate that this Airy function structure is universal across all M2-brane models and provide a general expression in terms of the equivariant volume of X, incorporating the mesonic deformations corresponding to complexified masses. This expression is then evaluated explicitly for several examples, including ABJM theory, its flavored generalizations, circular quivers, and beyond, demonstrating agreement with the available field theory localization results. We extend the analysis to the superconformal and twisted indices of M2-brane models, and their spindle generalizations, leaving their full perturbative completion for future work. Finally, we explore avenues for generalizing these results to other brane systems, explicitly applying the idea to D3-branes.
{"title":"M2-brane partition functions and HD supergravity from equivariant volumes","authors":"Luca Cassia, Kiril Hristov","doi":"10.1007/JHEP03(2026)100","DOIUrl":"10.1007/JHEP03(2026)100","url":null,"abstract":"<p>We use the results of our companion paper [<i>J. Phys. A</i> <b>58</b> (2025) 495201], which explores the equivariant generalization of the constant-map contribution in topological string theory on toric Calabi-Yau manifolds <i>X</i>, to establish a holographic correspondence with M2-brane partition functions. We rigorously test this conjecture within the perturbative regime, incorporating all finite <i>N</i> corrections on the field theory side. Our approach involves additional key details, such as incorporating effective 4d higher-derivative supergravity corrections to introduce refinement. A central result is the derivation of the Airy function representation for the squashed <i>S</i><sup>3</sup> partition function of the field theory, for an arbitrary squashing parameter. We demonstrate that this Airy function structure is universal across all M2-brane models and provide a general expression in terms of the equivariant volume of <i>X</i>, incorporating the mesonic deformations corresponding to complexified masses. This expression is then evaluated explicitly for several examples, including ABJM theory, its flavored generalizations, circular quivers, and beyond, demonstrating agreement with the available field theory localization results. We extend the analysis to the superconformal and twisted indices of M2-brane models, and their spindle generalizations, leaving their full perturbative completion for future work. Finally, we explore avenues for generalizing these results to other brane systems, explicitly applying the idea to D3-branes.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)100.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Symmetry-enriched topological (SET) phases combine intrinsic topological order with global symmetries, giving rise to novel symmetry phenomena. While SET phases with Abelian anyons are relatively well understood, those involving nonabelian anyons remain elusive. This obscurity stems from the multi-dimensional internal gauge spaces intrinsic to nonabelian anyons — a feature first made explicit in [1] and further explored in our recent works [2–7]. These internal spaces can transform in highly nontrivial ways under global symmetries. In this work, we employ an exactly solvable model — the multifusion Hu-Geer-Wu string-net model introduced in a companion paper [8] — to reveal how the internal gauge spaces of nonabelian anyons transform under symmetries. We uncover a universal phenomenon, global symmetry fragmentation (GSF), whereby symmetry-invariant anyons exhibit internal Hilbert space decompositions into eigensubspaces labeled by generally fractional symmetry charges. Meanwhile, symmetry-permuted anyons hybridize and fragment their internal spaces in accordance with their symmetry behavior. These fragmented structures realize genuinely nonlinear symmetry representations that transcend conventional linear and projective classifications. Our results identify nonlinear global symmetry fragmentation as a hallmark of SETs and may shed new light on symmetry-enabled control in topological quantum computation.
{"title":"Nonlinear symmetry-fragmentation of nonabelian anyons in symmetry-enriched topological phases: a string-net model realization","authors":"Nianrui Fu, Siyuan Wang, Yu Zhao, Yidun Wan","doi":"10.1007/JHEP03(2026)091","DOIUrl":"10.1007/JHEP03(2026)091","url":null,"abstract":"<p>Symmetry-enriched topological (SET) phases combine intrinsic topological order with global symmetries, giving rise to novel symmetry phenomena. While SET phases with Abelian anyons are relatively well understood, those involving nonabelian anyons remain elusive. This obscurity stems from the multi-dimensional internal gauge spaces intrinsic to nonabelian anyons — a feature first made explicit in [1] and further explored in our recent works [2–7]. These internal spaces can transform in highly nontrivial ways under global symmetries. In this work, we employ an exactly solvable model — the multifusion Hu-Geer-Wu string-net model introduced in a companion paper [8] — to reveal how the internal gauge spaces of nonabelian anyons transform under symmetries. We uncover a universal phenomenon, global symmetry fragmentation (GSF), whereby symmetry-invariant anyons exhibit internal Hilbert space decompositions into eigensubspaces labeled by generally fractional symmetry charges. Meanwhile, symmetry-permuted anyons hybridize and fragment their internal spaces in accordance with their symmetry behavior. These fragmented structures realize genuinely nonlinear symmetry representations that transcend conventional linear and projective classifications. Our results identify nonlinear global symmetry fragmentation as a hallmark of SETs and may shed new light on symmetry-enabled control in topological quantum computation.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)091.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}