We propose a new nonthermal leptogenesis mechanism triggered by the cosmic first-order phase transition. The Standard Model is extended with two generations of TeV-scale vectorlike leptons. The lighter generation gives rise to an inverse electroweak phase transition of the Higgs field at T ~ 200 GeV, restoring the symmetry, and resulting in relativistic bubble expansion in the space. The heavier generation is responsible for neutrino masses via the inverse seesaw mechanism. The interaction between bubble walls and particles in the plasma abundantly produces the vectorlike leptons, and they subsequently undergo CP-violating decay to generate the baryon asymmetry. This mechanism is testable at current and future particle experiments.
{"title":"When inverse seesaw meets inverse electroweak phase transition: a novel path to leptogenesis","authors":"Wen-Yuan Ai, Peisi Huang, Ke-Pan Xie","doi":"10.1007/JHEP02(2026)256","DOIUrl":"10.1007/JHEP02(2026)256","url":null,"abstract":"<p>We propose a new nonthermal leptogenesis mechanism triggered by the cosmic first-order phase transition. The Standard Model is extended with two generations of TeV-scale vectorlike leptons. The lighter generation gives rise to an <i>inverse</i> electroweak phase transition of the Higgs field at <i>T</i> ~ 200 GeV, restoring the symmetry, and resulting in relativistic bubble expansion in the space. The heavier generation is responsible for neutrino masses via the <i>inverse</i> seesaw mechanism. The interaction between bubble walls and particles in the plasma abundantly produces the vectorlike leptons, and they subsequently undergo CP-violating decay to generate the baryon asymmetry. This mechanism is testable at current and future particle experiments.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)256.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342514","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 precise measurement of the Higgs boson properties requires a robust framework to parametrize possible deviations from Standard Model (SM) predictions in the most model-independent way possible. The Effective Field Theory (EFT) framework has become the most widely used since it offers a broad scope and a consistent path to increase the precision of the computations. Two prominent EFTs are the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT). While similar in many aspects, their phenomenological differences are nowhere more pronounced than in multi-Higgs production. To precisely chart the separation between both EFTs, we study gluon-fusion double and triple Higgs production using bootstrapped on-shell amplitudes. This allows us to get the kinematic dependence of the gauge-invariant amplitude without field-redefinition ambiguities. As part of our study, we develop a technique that allows to build tree-level five-point on-shell amplitudes from lower-point on-shell amplitudes and bootstrapped contact terms. We then match the bootstrapped on-shell scattering amplitudes to the amplitudes computed in SMEFT (up to order 1/Λ4) and HEFT (at NNLO) and analyze the EFT order at which each kinematic structure appears. We also show how certain structures in gg → hhh appear only at dimension-12 in SMEFT or N3LO in HEFT.
{"title":"Multi-Higgs amplitudes bootstrapped: dissecting SMEFT and HEFT","authors":"Ramona Gröber, Alejo N. Rossia, Michał Ryczkowski","doi":"10.1007/JHEP02(2026)245","DOIUrl":"10.1007/JHEP02(2026)245","url":null,"abstract":"<p>The precise measurement of the Higgs boson properties requires a robust framework to parametrize possible deviations from Standard Model (SM) predictions in the most model-independent way possible. The Effective Field Theory (EFT) framework has become the most widely used since it offers a broad scope and a consistent path to increase the precision of the computations. Two prominent EFTs are the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT). While similar in many aspects, their phenomenological differences are nowhere more pronounced than in multi-Higgs production. To precisely chart the separation between both EFTs, we study gluon-fusion double and triple Higgs production using bootstrapped on-shell amplitudes. This allows us to get the kinematic dependence of the gauge-invariant amplitude without field-redefinition ambiguities. As part of our study, we develop a technique that allows to build tree-level five-point on-shell amplitudes from lower-point on-shell amplitudes and bootstrapped contact terms. We then match the bootstrapped on-shell scattering amplitudes to the amplitudes computed in SMEFT (up to order 1/Λ<sup>4</sup>) and HEFT (at NNLO) and analyze the EFT order at which each kinematic structure appears. We also show how certain structures in <i>gg</i> → <i>hhh</i> appear only at dimension-12 in SMEFT or N<sup>3</sup>LO in HEFT.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)245.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341666","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}
Lorentzian gravitational path integral for the Gauss-Bonnet gravity in 4D is studied in the mini-superspace ansatz for metric. The gauge-fixed path-integral for Robin boundary choice is computed exactly using Airy-functions, where the dominant contribution comes from No-boundary geometries. The lapse integral is further analysed using saddle-point methods to compare with exact results. Picard-Lefschetz methods are utilized to find the relevant complex saddles and deformed contour of integration, thereby using WKB method to compute the integral along the deformed contour in the saddle-point approximation. However, their successful application is possible only when system is devoid of degeneracies, which in present case appear in two types: type-1 where the flow-lines starting from neighbouring saddles overlap leading to ambiguities in deciding the relevance of saddles, type-2 where saddles merge for specific choices of boundary parameters leading to failure of WKB. Overcoming degeneracies using artificial defects introduces ambiguities due to the choice of defects involved. Corrections from quantum fluctuations of scale-factor overcome degeneracies only partially (lifts type-2 completely with partial resolution of type-1 ), with the residual lifted fluently by complex deformation of (Gℏ). Anti-linear symmetry present in various forms in the lapse action is the reason behind all the type-1 degeneracies. Any form of defect or deformation breaking anti-linearity resolves type-1 degeneracies, indicating complex deformation of (Gℏ) as an ideal choice. Compatibility with the KSW criterion is analyzed after symmetry breaking. Complex deformation of (Gℏ) modifies the KSW criterion, imposing a strong constraint on the deformation if No-boundary geometries are required to be always KSW-allowed.
{"title":"Resolving degeneracies in complex ℝ × S3 and θ-KSW","authors":"Manishankar Ailiga, Shubhashis Mallik, Gaurav Narain","doi":"10.1007/JHEP02(2026)249","DOIUrl":"10.1007/JHEP02(2026)249","url":null,"abstract":"<p>Lorentzian gravitational path integral for the Gauss-Bonnet gravity in 4<i>D</i> is studied in the mini-superspace ansatz for metric. The gauge-fixed path-integral for Robin boundary choice is computed exactly using <i>Airy</i>-functions, where the dominant contribution comes from No-boundary geometries. The lapse integral is further analysed using saddle-point methods to compare with exact results. Picard-Lefschetz methods are utilized to find the <i>relevant</i> complex saddles and deformed contour of integration, thereby using WKB method to compute the integral along the deformed contour in the saddle-point approximation. However, their successful application is possible only when system is devoid of degeneracies, which in present case appear in two types: <i>type-1</i> where the flow-lines starting from neighbouring saddles overlap leading to ambiguities in deciding the <i>relevance</i> of saddles, <i>type-2</i> where saddles merge for specific choices of boundary parameters leading to failure of WKB. Overcoming degeneracies using artificial <i>defects</i> introduces ambiguities due to the choice of <i>defects</i> involved. Corrections from quantum fluctuations of scale-factor overcome degeneracies only partially (lifts <i>type-2</i> completely with partial resolution of <i>type-1</i> ), with the residual lifted fluently by complex deformation of (<i>G</i>ℏ). <i>Anti-linear</i> symmetry present in various forms in the lapse action is the reason behind all the <i>type-1</i> degeneracies. Any form of <i>defect</i> or <i>deformation</i> breaking anti-linearity resolves <i>type-1</i> degeneracies, indicating complex deformation of (<i>G</i>ℏ) as an ideal choice. Compatibility with the KSW criterion is analyzed after symmetry breaking. Complex deformation of (<i>G</i>ℏ) modifies the KSW criterion, imposing a strong constraint on the deformation if No-boundary geometries are required to be always KSW-allowed.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)249.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341859","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 revisit the bulk Hilbert space interpretation of chords in the double-scaled SYK (DSSYK) model and introduce a notion of intertwiner that constructs bulk states from states with fixed boundary conditions. This leads to an isometric map that factorizes the one-particle bulk Hilbert space into a tensor product of two boundary Hilbert spaces without particle insertion. The map enables a systematic derivation of a family of correlation functions with arbitrary finite amount of matter insertions, relevant for capturing the switchback effect — a feature of holographic complexity. We further develop a path integral framework that describes multiple shockwave configurations in the semiclassical limit. For the two-body scattering processes in semi-classical regime, we show it exhibits sub-maximal chaos at finite temperature, consistent with the scramblon dynamics associated with the “fake disk” geometry. The effective “fake temperature” governing this behavior emerges from the semiclassical limit of the quantum 6j-symbol associated with the out-of-time-order correlator. We further analyze multi-shockwave configurations and derive precise conditions under which the switchback effect is realized, both in terms of the total chord number and the Krylov complexity of precursor operators. Our results clarify the structure of correlation functions with multiple operator insertions, their bulk interpretation in terms of shockwave geometries in the semi-classical regime, and provide a microscopic derivation of the switchback effect in the DSSYK model.
{"title":"Geometry of chord intertwiner, multiple shocks and switchback in double-scaled SYK","authors":"Sergio E. Aguilar-Gutierrez, Jiuci Xu","doi":"10.1007/JHEP02(2026)246","DOIUrl":"10.1007/JHEP02(2026)246","url":null,"abstract":"<p>We revisit the bulk Hilbert space interpretation of chords in the double-scaled SYK (DSSYK) model and introduce a notion of intertwiner that constructs bulk states from states with fixed boundary conditions. This leads to an isometric map that factorizes the one-particle bulk Hilbert space into a tensor product of two boundary Hilbert spaces without particle insertion. The map enables a systematic derivation of a family of correlation functions with arbitrary finite amount of matter insertions, relevant for capturing the switchback effect — a feature of holographic complexity. We further develop a path integral framework that describes multiple shockwave configurations in the semiclassical limit. For the two-body scattering processes in semi-classical regime, we show it exhibits sub-maximal chaos at finite temperature, consistent with the scramblon dynamics associated with the “fake disk” geometry. The effective “fake temperature” governing this behavior emerges from the semiclassical limit of the quantum 6<i>j</i>-symbol associated with the out-of-time-order correlator. We further analyze multi-shockwave configurations and derive precise conditions under which the switchback effect is realized, both in terms of the total chord number and the Krylov complexity of precursor operators. Our results clarify the structure of correlation functions with multiple operator insertions, their bulk interpretation in terms of shockwave geometries in the semi-classical regime, and provide a microscopic derivation of the switchback effect in the DSSYK model.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)246.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341669","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 initiate a systematic study of fragmentation energy correlators (FECs), which generalize traditional fragmentation functions and encode non-perturbative information about transverse dynamics in parton fragmentation processes. We define boost-invariant, non-perturbative FECs and derive a corresponding collinear factorization formula. A spin decomposition of the FECs is carried out, analogous to that of transverse-momentum-dependent fragmentation functions. In this work we focus particularly on the Collins-type quark FEC, which is sensitive to chiral symmetry breaking and characterizes the azimuthal asymmetry in the fragmentation of a transversely polarized quark. We perform a next-to-leading-order calculation of the corresponding hard coefficient in semi-inclusive deep-inelastic scattering for the quark non-singlet component, thereby validating the consistency of our theoretical framework.
{"title":"Collins-type fragmentation energy correlator in semi-inclusive deep inelastic lepton-hadron scattering","authors":"Qing-Hong Cao, Zhite Yu, C.-P. Yuan, Shu-Tao Zhang, Hua Xing Zhu","doi":"10.1007/JHEP02(2026)244","DOIUrl":"10.1007/JHEP02(2026)244","url":null,"abstract":"<p>We initiate a systematic study of fragmentation energy correlators (FECs), which generalize traditional fragmentation functions and encode non-perturbative information about transverse dynamics in parton fragmentation processes. We define boost-invariant, non-perturbative FECs and derive a corresponding collinear factorization formula. A spin decomposition of the FECs is carried out, analogous to that of transverse-momentum-dependent fragmentation functions. In this work we focus particularly on the Collins-type quark FEC, which is sensitive to chiral symmetry breaking and characterizes the azimuthal asymmetry in the fragmentation of a transversely polarized quark. We perform a next-to-leading-order calculation of the corresponding hard coefficient in semi-inclusive deep-inelastic scattering for the quark non-singlet component, thereby validating the consistency of our theoretical framework.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)244.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341667","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}
In this paper we investigate the finite N exact values of the S3 partition function of the ( mathcal{N} ) = 4 super Yang-Mills theory with one adjoint hypermultiplet and Nf fundamental hypermultiplets, which describes N M2-branes on ( {mathbb{C}}^2times {mathbb{C}}^2/{mathbb{Z}}_{N_{textrm{f}}} ), with mass and FI deformations. We claim that the grand canonical sum of the partition function obeys a bilinear difference relation with respect to the shifts of the mass parameters of the fundamental hypermultiplets, which results in a new recursion relation for the partition function with respect to N. As an application, we also determine the analytic expression for the leading 1/N non-perturbative correction to the free energy of these models, which would correspond holographically to the contribution from an M2-brane wrapped on a 3d volume in the internal space of AdS4×S7/( {mathbb{Z}}_{N_{textrm{f}}} ).
{"title":"New recursion relations for M2-brane matrix models","authors":"Bin He, Tomoki Nosaka","doi":"10.1007/JHEP02(2026)243","DOIUrl":"10.1007/JHEP02(2026)243","url":null,"abstract":"<p>In this paper we investigate the finite <i>N</i> exact values of the <i>S</i><sup>3</sup> partition function of the <span>( mathcal{N} )</span> = 4 super Yang-Mills theory with one adjoint hypermultiplet and <i>N</i><sub>f</sub> fundamental hypermultiplets, which describes <i>N</i> M2-branes on <span>( {mathbb{C}}^2times {mathbb{C}}^2/{mathbb{Z}}_{N_{textrm{f}}} )</span>, with mass and FI deformations. We claim that the grand canonical sum of the partition function obeys a bilinear difference relation with respect to the shifts of the mass parameters of the fundamental hypermultiplets, which results in a new recursion relation for the partition function with respect to <i>N</i>. As an application, we also determine the analytic expression for the leading 1/<i>N</i> non-perturbative correction to the free energy of these models, which would correspond holographically to the contribution from an M2-brane wrapped on a 3d volume in the internal space of AdS<sub>4</sub>×<i>S</i><sup>7</sup>/<span>( {mathbb{Z}}_{N_{textrm{f}}} )</span>.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)243.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341861","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}
In this article, we investigate the proposed duality between the island and the defect extremal surface (DES) prescriptions using the fine-grained entanglement entropy in Karch-Randall (KR) brane-world models with gravitating radiation baths. We consider the AdS3 black string geometry and compute the entanglement entropy for radiation subsystems on an AdS2 eternal black hole background using both the island and the DES prescriptions. We find an agreement between the two proposals for the island and the no-island phases, thus verifying the validity of the proposed duality. We further extend to a ( Toverline{T} ) deformed AdS3 black string geometry with a cut-off and find consistent results for both phases. We finally plot and compare the Page curves for the undeformed and deformed scenarios, and discuss the modifications due to ( Toverline{T} ) deformation.
{"title":"Entanglement, defects, and ( Toverline{T} ) on a black hole background","authors":"Ankur Dey","doi":"10.1007/JHEP02(2026)242","DOIUrl":"10.1007/JHEP02(2026)242","url":null,"abstract":"<p>In this article, we investigate the proposed duality between the island and the defect extremal surface (DES) prescriptions using the fine-grained entanglement entropy in Karch-Randall (KR) brane-world models with gravitating radiation baths. We consider the AdS<sub>3</sub> black string geometry and compute the entanglement entropy for radiation subsystems on an AdS<sub>2</sub> eternal black hole background using both the island and the DES prescriptions. We find an agreement between the two proposals for the island and the no-island phases, thus verifying the validity of the proposed duality. We further extend to a <span>( Toverline{T} )</span> deformed AdS<sub>3</sub> black string geometry with a cut-off and find consistent results for both phases. We finally plot and compare the Page curves for the undeformed and deformed scenarios, and discuss the modifications due to <span>( Toverline{T} )</span> deformation.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)242.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341862","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}
In this work, we study the holographic entanglement entropy (HEE) and holographic complexity (HC) for three-dimensional dyonic quantum black holes, incorporating corrections arising from bulk quantum fields in the setup of double holography. We investigate the holographic entanglement entropy through the holographic Ryu-Takayanagi (RT) prescription and the island prescription. Using RT extremization, we evaluate HEE for connected and disconnected (island) surfaces and show islands emerge when RT surfaces intersect the brane; entanglement entropy grows with subregion size and ultimately saturates for quantum black holes as well as dressed defects. For complexity, we analyze both CV (perturbative) and CA (exact, all-orders) prescriptions: the leading quantum corrections feature universal behavior and the late-time growth can be expressed in thermodynamic variables, obeying generalized Lloyd-type bounds. In contrast, quantum dressed defects exhibit vanishing late-time growth. The CA prescription proves to be more tractable nonperturbatively and yields a thermodynamic interpretation of complexity growth.
{"title":"Entanglement entropy and complexity in dyonic quantum black holes","authors":"Sanhita Parihar, Gurmeet Singh Punia","doi":"10.1007/JHEP02(2026)248","DOIUrl":"10.1007/JHEP02(2026)248","url":null,"abstract":"<p>In this work, we study the holographic entanglement entropy (HEE) and holographic complexity (HC) for three-dimensional dyonic quantum black holes, incorporating corrections arising from bulk quantum fields in the setup of double holography. We investigate the holographic entanglement entropy through the holographic Ryu-Takayanagi (RT) prescription and the island prescription. Using RT extremization, we evaluate HEE for connected and disconnected (island) surfaces and show islands emerge when RT surfaces intersect the brane; entanglement entropy grows with subregion size and ultimately saturates for quantum black holes as well as dressed defects. For complexity, we analyze both CV (perturbative) and CA (exact, all-orders) prescriptions: the leading quantum corrections feature universal behavior and the late-time growth can be expressed in thermodynamic variables, obeying generalized Lloyd-type bounds. In contrast, quantum dressed defects exhibit vanishing late-time growth. The CA prescription proves to be more tractable nonperturbatively and yields a thermodynamic interpretation of complexity growth.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)248.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341668","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}
Stefano Baiguera, Nicolas Chagnet, Shira Chapman, Osher Shoval
Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous studies have primarily focused on cases where all generators of the conformal group contribute equally to the cost of building a circuit. In this work, we present a general framework for studying the complexity of circuits in generic Lie groups, where penalty factors assign relative weights to different generators. Our approach constructs a metric on the coset space of quantum states, induced from a (pseudo-)Riemannian norm on the space of unitary circuits. The geodesics of this metric are interpreted as optimal circuits. The method builds on the formalism of (pseudo-)Riemannian submersions and connects naturally to other prescriptions in the literature, including cost function minimization along stabilizer directions and constructions based on coadjoint orbits. As a concrete application, we compute state complexity for states in one- and two-dimensional CFTs. For specific choices of penalty factors, our prescription yields a positive-definite metric with a viable interpretation as complexity; in other cases, the resulting metric is indefinite. In the viable regime, we derive analytic results when a specific penalty factor is turned off, develop perturbative expansions for small values of the penalty factors, and provide numerical results in the general case. We comment on the relation of our measure of complexity to holography.
{"title":"CFT complexity and penalty factors","authors":"Stefano Baiguera, Nicolas Chagnet, Shira Chapman, Osher Shoval","doi":"10.1007/JHEP02(2026)247","DOIUrl":"10.1007/JHEP02(2026)247","url":null,"abstract":"<p>Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous studies have primarily focused on cases where all generators of the conformal group contribute equally to the cost of building a circuit. In this work, we present a general framework for studying the complexity of circuits in generic Lie groups, where penalty factors assign relative weights to different generators. Our approach constructs a metric on the coset space of quantum states, induced from a (pseudo-)Riemannian norm on the space of unitary circuits. The geodesics of this metric are interpreted as optimal circuits. The method builds on the formalism of (pseudo-)Riemannian submersions and connects naturally to other prescriptions in the literature, including cost function minimization along stabilizer directions and constructions based on coadjoint orbits. As a concrete application, we compute state complexity for states in one- and two-dimensional CFTs. For specific choices of penalty factors, our prescription yields a positive-definite metric with a viable interpretation as complexity; in other cases, the resulting metric is indefinite. In the viable regime, we derive analytic results when a specific penalty factor is turned off, develop perturbative expansions for small values of the penalty factors, and provide numerical results in the general case. We comment on the relation of our measure of complexity to holography.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)247.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341860","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}
Dark Matter (DM) is a known unknown. Apart, current experimental constraints on flavor-changing neutral current (FCNC) processes involving up-type quarks also provide scope to explore physics beyond the Standard Model (SM). In this article, we establish a connection between the flavor sector and the DM sector with minimal extension of the SM. Here a singlet complex scalar field, stable under ( {mathcal{Z}}_3 ) symmetry, acts as DM and couples to SM up-type quarks through a heavy Dirac vector-like quark (VLQ), which shares the same ( {mathcal{Z}}_3 ) charge as of the DM. The model is compatible with the observed ( {D}^0-{overline{D}}^0 ) mixing, top-FCNC interactions, and D0 meson decays, together with DM relic density, while evading the direct and indirect DM search bounds. The model can be probed at the future high-energy muon collider, through distinctive signatures of VLQ production, where the VLQ decays into DM and SM particles, abiding by the existing bounds.
{"title":"Up-type FCNC in presence of Dark Matter","authors":"Subhaditya Bhattacharya, Lipika Kolay, Dipankar Pradhan, Abhik Sarkar","doi":"10.1007/JHEP02(2026)239","DOIUrl":"10.1007/JHEP02(2026)239","url":null,"abstract":"<p>Dark Matter (DM) is a known unknown. Apart, current experimental constraints on flavor-changing neutral current (FCNC) processes involving up-type quarks also provide scope to explore physics beyond the Standard Model (SM). In this article, we establish a connection between the flavor sector and the DM sector with minimal extension of the SM. Here a singlet complex scalar field, stable under <span>( {mathcal{Z}}_3 )</span> symmetry, acts as DM and couples to SM up-type quarks through a heavy Dirac vector-like quark (VLQ), which shares the same <span>( {mathcal{Z}}_3 )</span> charge as of the DM. The model is compatible with the observed <span>( {D}^0-{overline{D}}^0 )</span> mixing, top-FCNC interactions, and <i>D</i><sup>0</sup> meson decays, together with DM relic density, while evading the direct and indirect DM search bounds. The model can be probed at the future high-energy muon collider, through distinctive signatures of VLQ production, where the VLQ decays into DM and SM particles, abiding by the existing bounds.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)239.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341744","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}