{"title":"Updating the holomorphic modular bootstrap","authors":"Suresh Govindarajan, Akhila Sadanandan","doi":"10.1007/JHEP08(2026)216","DOIUrl":"10.1007/JHEP08(2026)216","url":null,"abstract":"<p>We update the holomorphic modular bootstrap incorporating a recent result that computes the exact <i>S</i>-matrix within the Modular Linear Differential Equation (MLDE) setting. Further, using knowledge of the allowed exponents modulo one, we obtain admissible solutions to all MLDE’s with up to six characters and Wronskian index < 6 and one accessory parameter with <i>c</i><sub>eff</sub> ≤ 24. We then identify which of the admissible solutions have good fusion rules — we call such solutions <i>tenable</i>. When possible, we identify the CFT and in the unitary cases the MTC class they belong to.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)216.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837541","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}
{"title":"An intermediate scale R-axion & the QCD axion","authors":"James Unwin","doi":"10.1007/JHEP08(2026)208","DOIUrl":"10.1007/JHEP08(2026)208","url":null,"abstract":"<p>An intermediate scale R-axion faces an immediate obstruction from the Dine-Festuccia-Komargodski (DFK) bound on the superpotential, 2|⟨<i>W</i>⟩| ≤ <i>f</i><sub><i>R</i></sub><i>F</i>, since for a nearly Minkowski vacuum it typically follows that <i>f</i><sub><i>R</i></sub> ≳ <i>M</i><sub>Pl</sub>. We show that this lower bound on <i>f</i><sub><i>R</i></sub> can be relaxed in an effective construction with the scalar potential tuned near zero via a mixed <i>F</i>- and <i>D</i>-term uplift, leading to a metastable vacuum in which the usual Planckian-<i>f</i><sub><i>R</i></sub> inference from the DFK argument is avoided locally. Validity of the effective field theory and metastability of the small <i>f</i><sub><i>R</i></sub> vacuum generically both imply a relaxed bound: <span>( {f}_Rgtrsim sqrt{m_{3/2}{M}_{mathrm{Pl}}} )</span>. We also highlight that if the R-symmetry has a QCD anomaly, this potentially permits the R-axion to play the role of the QCD axion. TeV-scale supersymmetry permits <i>f</i><sub><i>R</i></sub> ~ 10<sup>11</sup> GeV, this not only evades certain astrophysical and cosmological axion constraints, but notably lies in the window for which the observed dark matter abundance can be reproduced by the R-axion via the misalignment mechanism.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)208.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837726","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}
{"title":"Holographic equidistribution","authors":"Nico Cooper","doi":"10.1007/JHEP08(2026)212","DOIUrl":"10.1007/JHEP08(2026)212","url":null,"abstract":"<p>Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of the AdS<sub>3</sub>/RMT<sub>2</sub> program. We use an equidistribution theorem for Hecke operators to show that in each of these large <i>N</i> limits, an entire heavy sector of the partition function gets integrated out, leaving only contributions from Poincaré series of light states. This gives an immediate holographic interpretation as a sum over semiclassical handlebody geometries. We speculate on further physical interpretations for equidistribution, including a potential ergodicity statement.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)212.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837741","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}
{"title":"Holographic equidistribution","authors":"Nico Cooper","doi":"10.1007/JHEP08(2026)212","DOIUrl":"10.1007/JHEP08(2026)212","url":null,"abstract":"<p>Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of the AdS<sub>3</sub>/RMT<sub>2</sub> program. We use an equidistribution theorem for Hecke operators to show that in each of these large <i>N</i> limits, an entire heavy sector of the partition function gets integrated out, leaving only contributions from Poincaré series of light states. This gives an immediate holographic interpretation as a sum over semiclassical handlebody geometries. We speculate on further physical interpretations for equidistribution, including a potential ergodicity statement.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)212.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837754","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}
Marco Ardu, Lorenzo Calibbi, Marco Fedele, Federico Mescia
{"title":"ALP production in lepton flavour violating meson, tau and gauge boson decays","authors":"Marco Ardu, Lorenzo Calibbi, Marco Fedele, Federico Mescia","doi":"10.1007/JHEP08(2026)217","DOIUrl":"10.1007/JHEP08(2026)217","url":null,"abstract":"<p>In this paper we study axion-like particles (ALPs) with lepton-flavour-violating (LFV) couplings in the mass regime above the muon threshold, <i>m</i><sub><i>a</i></sub> > <i>m</i><sub><i>μ</i></sub>, where the strong bound from the exotic muon decay <i>μ</i> → <i>ea</i> no longer apply and the decay channel <i>a</i> → <i>eμ</i> becomes kinematically accessible. In this region, the ALP typically decays promptly, motivating new search strategies based on its production in decays involving virtual muons. We analyse charged-meson and <i>W</i> decays, neutral-current processes such as <i>Z</i> and quarkonium decays, and, when couplings to the third generation are present, LFV <i>τ</i> decays. The subsequent decay <i>a</i> → <i>eμ</i> leads to striking LFV signatures with negligible Standard Model backgrounds. Combining these production modes with current low-energy constraints, we assess the sensitivity of future high-energy <i>e</i><sup>+</sup><i>e</i><sup>−</sup> colliders, flavour factories such as Belle II and STCF, fixed-target experiments such as NA62, and proton beam-dump facilities such as SHiP. Overall, our results identify LFV ALP production in meson, gauge-boson, quarkonium and <i>τ</i> decays (with displaced vertices) as a promising and largely unexplored avenue to test ALP interactions with charged leptons above the muon mass threshold.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)217.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837945","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}
{"title":"Unimodular time in JT gravity: a holographic clock","authors":"Altay Etkin, Farbod-Sayyed Rassouli","doi":"10.1007/JHEP08(2026)193","DOIUrl":"10.1007/JHEP08(2026)193","url":null,"abstract":"<p>How is a “bulk clock” encoded holographically? We address this in Jackiw-Teitelboim (JT) gravity, where a natural physical clock emerges by promoting the vacuum energy to a dynamical variable: the vacuum cosmological constant becomes a top form degree of freedom conjugate to spacetime volume, thereby defining a notion of bulk physical time. This construction is naturally formulated in the Henneaux-Teitelboim (HT) framework. We show that the boundary dynamics is the Schwarzian mode coupled to a free particle on U(1), matching the universal low-energy effective action of the complex SYK model. By further clarifying the role of the vacuum cosmological constant as a top form, we establish the equivalence between JT gravity coupled to two-dimensional Maxwell theory and 2d HT gravity via an explicit field redefinition. The initial question is addressed: we show that the resulting boundary theory can itself be rewritten as an observer action, equivalently a (0 + 1)-dimensional HT theory. This yields a direct identification of the boundary clock with the U(1) phase mode, and makes its relation to the bulk clock explicit.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)193.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837594","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}
Luca Griguolo, Jacopo Papalini, Lorenzo Russo, Domenico Seminara
{"title":"A new perspective on dilaton gravity at finite cutoff","authors":"Luca Griguolo, Jacopo Papalini, Lorenzo Russo, Domenico Seminara","doi":"10.1007/JHEP08(2026)197","DOIUrl":"10.1007/JHEP08(2026)197","url":null,"abstract":"<p>The formulation of two-dimensional quantum gravity at finite cutoff remains an open problem. We revisit this question in JT gravity from two perspectives: the closed-channel bulk path integral and the path integral over boundary curves. First, we study the radial evolution of a closed universe and derive the trumpet wavefunction as a transition amplitude between a geodesic boundary and a finite Dirichlet boundary. Our analysis recovers the Hartle-Hawking wavefunction without imposing asymptotic boundary conditions, allowing the trumpet to be glued to a cap wavefunction to reconstruct the smooth disk. Second, we derive an exact Riccati equation for the extrinsic curvature of a finite-cutoff boundary curve in the Euclidean Poincaré disk. A WKB expansion of this equation yields all perturbative corrections in the cutoff parameter and captures nonperturbative effects. From this, we compute the quadratic boundary action and the one-loop partition function at finite cutoff, finding agreement with both the bulk approach and the expected one-loop effective action for the <span>( Toverline{T} )</span> deformation of the Schwarzian theory. Extracting lessons from JT gravity, we then argue that similar relationships hold for general dilaton gravities with arbitrary potentials <i>V</i> (<i>ϕ</i>) and propose an exact expression for their finite cutoff partition functions. We finally investigate several signatures of UV completeness in these settings, introducing a canonical quantization approach within the finite cutoff framework.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)197.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837936","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}
{"title":"The effects of a scalar singlet leptoquark at the Z factory","authors":"Dazhuang He, Yu Zhang, Hao Sun","doi":"10.1007/JHEP08(2026)199","DOIUrl":"10.1007/JHEP08(2026)199","url":null,"abstract":"<p>We evaluate the observability of the effects of a scalar singlet leptoquark (LQ) in <i>μ</i> and <i>τ</i>-pair productions at the <i>Z</i> factory. In the scenario addressing the charged-current anomalies, the LQ contributions to <i>μ</i>-pair final state are negligible. In contrast, a sizable contribution arises in the <i>τ</i>-pair production, which is identical in both <i>Z</i> decay and <i>e</i><sup>+</sup><i>e</i><sup><i>−</i></sup> collider at <i>Z</i> pole. These effects are mainly sensitive to left-handed interaction, showing a maximum deviation of about −0<i>.</i>7% for both 1 TeV and 2 TeV LQ. The suppression of new physics effects from the heavy LQ can be compensated by the enlarged couplings parameter space. For the <i>τ</i>-pair production channel, we further specify the coupling constraints corresponding to the expected measurement precision at the future <i>Z</i> factory. Moreover, we provide an analytic function in terms of the LQ mass and couplings to quantify the LQ effects. The differential distributions in the collision process indicate that the LQ effects remain stable throughout the kinematic region. Meanwhile, the measurement sensitivity of the <i>τ</i>-pair final state at the future <i>Z</i> factory is expected to impose further constraints on the LQ theory.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)199.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837452","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}
Luca Griguolo, Jacopo Papalini, Lorenzo Russo, Domenico Seminara
{"title":"A new perspective on dilaton gravity at finite cutoff","authors":"Luca Griguolo, Jacopo Papalini, Lorenzo Russo, Domenico Seminara","doi":"10.1007/JHEP08(2026)197","DOIUrl":"10.1007/JHEP08(2026)197","url":null,"abstract":"<p>The formulation of two-dimensional quantum gravity at finite cutoff remains an open problem. We revisit this question in JT gravity from two perspectives: the closed-channel bulk path integral and the path integral over boundary curves. First, we study the radial evolution of a closed universe and derive the trumpet wavefunction as a transition amplitude between a geodesic boundary and a finite Dirichlet boundary. Our analysis recovers the Hartle-Hawking wavefunction without imposing asymptotic boundary conditions, allowing the trumpet to be glued to a cap wavefunction to reconstruct the smooth disk. Second, we derive an exact Riccati equation for the extrinsic curvature of a finite-cutoff boundary curve in the Euclidean Poincaré disk. A WKB expansion of this equation yields all perturbative corrections in the cutoff parameter and captures nonperturbative effects. From this, we compute the quadratic boundary action and the one-loop partition function at finite cutoff, finding agreement with both the bulk approach and the expected one-loop effective action for the <span>( Toverline{T} )</span> deformation of the Schwarzian theory. Extracting lessons from JT gravity, we then argue that similar relationships hold for general dilaton gravities with arbitrary potentials <i>V</i> (<i>ϕ</i>) and propose an exact expression for their finite cutoff partition functions. We finally investigate several signatures of UV completeness in these settings, introducing a canonical quantization approach within the finite cutoff framework.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)197.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837869","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}
{"title":"On cosmological singularities in string theory","authors":"Jinwei Chu, David Kutasov","doi":"10.1007/JHEP08(2026)195","DOIUrl":"10.1007/JHEP08(2026)195","url":null,"abstract":"<p>We study the time evolution of a 3 + 1 dimensional spacetime, where space is a large three-sphere, due to small perturbations of the background fields. We focus on two classes of deformations. One corresponds on the worldsheet to time-dependent non-abelian Thirring deformations. The other to perturbations of the radius of the three-sphere. In the former case, we find that small deformations generically lead to big-bang and big-crunch singularities, near which the spacetime becomes highly anisotropic. We argue that string theory likely resolves these singularities. In the latter case, general solutions have the property that the radius of the three-sphere goes to infinity at a finite time, but there are no solutions in which it collapses to zero. We also discuss the interplay of these spacetime properties with the corresponding worldsheet RG flows.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 8","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP08(2026)195.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837443","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}