Santiago Agüí Salcedo, Thomas Colas, Lennard Dufner, Enrico Pajer
Several major open problems in cosmology — including the nature of inflation, dark matter, and dark energy — share a common structure: they involve spacetime-filling media with unknown microphysics, and can be probed so far only through their gravitational effects. This observation motivates a systematic open-system approach to cosmology, in which gravity evolves in the presence of a generic, unobservable environment. In this work, we develop a general framework for open gravitational dynamics based on general relativity and the Schwinger-Keldysh formalism, carefully addressing the nontrivial constraints imposed by diffeomorphism invariance. At the quantum level, our path integral formulation computes the gravitational density matrix in perturbation theory around a semi-classical spacetime.
As illustrative applications, we study inflation and the propagation of gravitational waves in classical regimes where environmental interactions are non-negligible. In the inflationary context, our framework reproduces the known Open Effective Field Theory of Inflation in the decoupling limit and extends it to include gravitational interactions. For gravitational waves, we derive the most general conservative and dissipative corrections to propagation. Remarkably, we find that the leading-order gravitational birefringence is dissipative in nature, whereas conservative birefringence appears only at higher derivative order — opposite to the electromagnetic case. Our results pave the way to modeling dissipative effects in the late universe.
{"title":"An open system approach to gravity","authors":"Santiago Agüí Salcedo, Thomas Colas, Lennard Dufner, Enrico Pajer","doi":"10.1007/JHEP02(2026)241","DOIUrl":"10.1007/JHEP02(2026)241","url":null,"abstract":"<p>Several major open problems in cosmology — including the nature of inflation, dark matter, and dark energy — share a common structure: they involve spacetime-filling media with unknown microphysics, and can be probed so far only through their gravitational effects. This observation motivates a systematic open-system approach to cosmology, in which gravity evolves in the presence of a generic, unobservable environment. In this work, we develop a general framework for open gravitational dynamics based on general relativity and the Schwinger-Keldysh formalism, carefully addressing the nontrivial constraints imposed by diffeomorphism invariance. At the quantum level, our path integral formulation computes the gravitational density matrix in perturbation theory around a semi-classical spacetime.</p><p>As illustrative applications, we study inflation and the propagation of gravitational waves in classical regimes where environmental interactions are non-negligible. In the inflationary context, our framework reproduces the known Open Effective Field Theory of Inflation in the decoupling limit and extends it to include gravitational interactions. For gravitational waves, we derive the most general conservative and dissipative corrections to propagation. Remarkably, we find that the leading-order gravitational birefringence is dissipative in nature, whereas conservative birefringence appears only at higher derivative order — opposite to the electromagnetic case. Our results pave the way to modeling dissipative effects in the late universe.</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)241.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341749","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 complete the derivation of the dressing factors for the AdS3 × S3 × T4 S matrix with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux, in the “string” and “mirror” kinematics. Using these, we propose the mirror Thermodynamic Bethe Ansatz equations which describe the spectrum of the model at any string tension.
{"title":"Dressing factors and mirror thermodynamic Bethe ansatz for mixed-flux AdS3/CFT2","authors":"Sergey Frolov, Davide Polvara, Alessandro Sfondrini","doi":"10.1007/JHEP02(2026)237","DOIUrl":"10.1007/JHEP02(2026)237","url":null,"abstract":"<p>We complete the derivation of the dressing factors for the <i>AdS</i><sub>3</sub> × <i>S</i><sup>3</sup> × <i>T</i><sup>4</sup> S matrix with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux, in the “string” and “mirror” kinematics. Using these, we propose the mirror Thermodynamic Bethe Ansatz equations which describe the spectrum of the model at any string tension.</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)237.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341740","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}
Motivated by the stringent experimental bounds on proton lifetime and the need for precise low-energy predictions, there has been renewed interest in the renormalization group (RG) evolution of Wilson coefficients for baryon number violating (BNV) operators and their characteristic new-physics scales. In this work, we analyze the RG running of dimension-6 four-fermion operators in the ( overline{textrm{MS}} ) scheme that mediate nucleon decay channels such as p → e+π0, while systematically accounting for the impact of baryon number conserving (BNC) new-physics that can enter the theory at an intermediate scale as higher-dimensional effective field theory operators. These BNC operators mix with BNV ones at 1-loop and alter the RG flow. The running is performed from the electroweak scale up to representative intermediate scales of 104 GeV, 106 GeV, and 109 GeV, corresponding to possible thresholds for new BNC degrees of freedom. Comparing the RG evolved coefficients with current experimental bounds on nucleon decay lifetimes, we find that the inclusion of BNC-BNV mixing, dominated by top quark loops, can significantly lower the effective proton decay scale to ∼ 107 GeV, thus mitigating the need of a large desert. A Python package (Available at: https://github.com/rp-winter/Nucleon-Decay-SMEFT) is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.
{"title":"RG evolution and effect of intermediate new-physics on ∆B = 1 four-fermion operators","authors":"Mathew Thomas Arun, M Shyam, Ritik Pal","doi":"10.1007/JHEP02(2026)238","DOIUrl":"10.1007/JHEP02(2026)238","url":null,"abstract":"<p>Motivated by the stringent experimental bounds on proton lifetime and the need for precise low-energy predictions, there has been renewed interest in the renormalization group (RG) evolution of Wilson coefficients for baryon number violating (BNV) operators and their characteristic new-physics scales. In this work, we analyze the RG running of dimension-6 four-fermion operators in the <span>( overline{textrm{MS}} )</span> scheme that mediate nucleon decay channels such as <i>p</i> → <i>e</i><sup>+</sup><i>π</i><sup>0</sup>, while systematically accounting for the impact of baryon number conserving (BNC) new-physics that can enter the theory at an intermediate scale as higher-dimensional effective field theory operators. These BNC operators mix with BNV ones at 1-loop and alter the RG flow. The running is performed from the electroweak scale up to representative intermediate scales of 10<sup>4</sup> GeV, 10<sup>6</sup> GeV, and 10<sup>9</sup> GeV, corresponding to possible thresholds for new BNC degrees of freedom. Comparing the RG evolved coefficients with current experimental bounds on nucleon decay lifetimes, we find that the inclusion of BNC-BNV mixing, dominated by top quark loops, can significantly lower the effective proton decay scale to ∼ 10<sup>7</sup> GeV, thus mitigating the need of a large desert. A Python package (Available at: https://github.com/rp-winter/Nucleon-Decay-SMEFT) is provided to facilitate the RG evolution of nucleon-decay Wilson coefficients, allowing for the inclusion of generic BNC effects.</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)238.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341745","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}
Markus A. G. Amano, Minoru Eto, Muneto Nitta, Shin Sasaki
We investigate the chiral soliton lattice (CSL) in the framework of holographic QCD in magnetic field. Under appropriate boundary conditions for the gauge field and the quark mass deformation, we demonstrate that the ground state in the gravitational dual of QCD is given by the CSL in the background magnetic field and the baryon number density. In the presence of the background magnetic field, we show that the CSL is interpreted as a uniformly distributed D4-branes in the holographic setup, where the chiral soliton is identified with a non-self-dual instanton vortex or a center vortex in the five dimensional bulk gauge theory. While the baryon numbers are given to chiral solitons as well as Skyrmions due to the different terms in the Wess-Zumino-Witten (WZW) term in the chiral perturbation theory, these baryon numbers with different origins are unified in terms of the instanton charge density in five dimensions. With bulk analysis of the WZW term, we find that the pion decay constant becomes dependent on the magnetic field. For the massless pion case, we obtain an analytical form that is in qualitative agreement with lattice QCD results for strong magnetic fields.
{"title":"Holographic QCD matter: chiral soliton lattices in strong magnetic field","authors":"Markus A. G. Amano, Minoru Eto, Muneto Nitta, Shin Sasaki","doi":"10.1007/JHEP02(2026)240","DOIUrl":"10.1007/JHEP02(2026)240","url":null,"abstract":"<p>We investigate the chiral soliton lattice (CSL) in the framework of holographic QCD in magnetic field. Under appropriate boundary conditions for the gauge field and the quark mass deformation, we demonstrate that the ground state in the gravitational dual of QCD is given by the CSL in the background magnetic field and the baryon number density. In the presence of the background magnetic field, we show that the CSL is interpreted as a uniformly distributed D4-branes in the holographic setup, where the chiral soliton is identified with a non-self-dual instanton vortex or a center vortex in the five dimensional bulk gauge theory. While the baryon numbers are given to chiral solitons as well as Skyrmions due to the different terms in the Wess-Zumino-Witten (WZW) term in the chiral perturbation theory, these baryon numbers with different origins are unified in terms of the instanton charge density in five dimensions. With bulk analysis of the WZW term, we find that the pion decay constant becomes dependent on the magnetic field. For the massless pion case, we obtain an analytical form that is in qualitative agreement with lattice QCD results for strong magnetic fields.</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)240.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341746","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}
Beatrix Mühlmann, Vladimir Narovlansky, Ioannis Tsiares
We use analytic (super-)conformal bootstrap methods to derive explicit expressions for the structure constants of ( mathcal{N} ) = 1 Liouville CFT in the ‘timelike’ regime of the superconformal central charge. The obtained expressions take the form of inverses of the appropriate spacelike counterparts, which we explain concretely by elucidating the analytic properties of the corresponding shift relations in the NS- and R-sectors for the normalization-independent bootstrap data on the sphere. In a particular normalization, the timelike structure constants are shown to agree with the OPE coefficients of ( mathcal{N} ) = 1 Minimal Models when specified at degenerate values of the momenta, exactly as in the non-supersymmetric case. We discuss possible applications of our results, with emphasis on the construction of the ( mathcal{N} ) = 1 supersymmetric analog of the Virasoro Minimal String.
{"title":"On the three-point functions in timelike ( mathcal{N} ) = 1 Liouville CFT","authors":"Beatrix Mühlmann, Vladimir Narovlansky, Ioannis Tsiares","doi":"10.1007/JHEP02(2026)236","DOIUrl":"10.1007/JHEP02(2026)236","url":null,"abstract":"<p>We use analytic (super-)conformal bootstrap methods to derive explicit expressions for the structure constants of <span>( mathcal{N} )</span> = 1 Liouville CFT in the ‘timelike’ regime of the superconformal central charge. The obtained expressions take the form of inverses of the appropriate spacelike counterparts, which we explain concretely by elucidating the analytic properties of the corresponding shift relations in the NS- and R-sectors for the normalization-independent bootstrap data on the sphere. In a particular normalization, the timelike structure constants are shown to agree with the OPE coefficients of <span>( mathcal{N} )</span> = 1 Minimal Models when specified at degenerate values of the momenta, exactly as in the non-supersymmetric case. We discuss possible applications of our results, with emphasis on the construction of the <span>( mathcal{N} )</span> = 1 supersymmetric analog of the Virasoro Minimal String.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)236.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341146","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 investigate the dynamics of the entanglement Hamiltonian in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal field theory, we obtain a local expression where the left- and right-moving components of the energy density are associated with different weight functions. The results are then compared to numerical calculations for the hopping chain, which requires to consider a proper continuum limit of the lattice entanglement Hamiltonian, obtaining a good agreement with the field-theory prediction.
{"title":"Entanglement Hamiltonian after a local quench","authors":"Riccarda Bonsignori, Viktor Eisler","doi":"10.1007/JHEP02(2026)232","DOIUrl":"10.1007/JHEP02(2026)232","url":null,"abstract":"<p>We investigate the dynamics of the entanglement Hamiltonian in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal field theory, we obtain a local expression where the left- and right-moving components of the energy density are associated with different weight functions. The results are then compared to numerical calculations for the hopping chain, which requires to consider a proper continuum limit of the lattice entanglement Hamiltonian, obtaining a good agreement with the field-theory prediction.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)232.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341150","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 computation of the classical gravitational waveform for a particle moving in a plane wave background using on-shell amplitudes. We emphasize the relationship between gravitational memory and the boundary conditions of external scattering states, which were neglected in previous works. We then provide the first tree-level expression for the waveform that captures all memory effects. The waveform is presented in terms of Synge’s world function, with explicit tail terms, and a smooth weak memory limit. We also discuss the choice of BMS frame for the waveform on a plane wave background. In flat space, this corresponds to a choice of soft dressing of the initial state. We show that on a plane wave background, this dressing becomes a supertranslation of the waveform, in addition to a phase shift in the waveshape of the background.
{"title":"Memory and supertranslations on plane wave spacetimes: an on-shell perspective","authors":"Andrea Cristofoli, Sonja Klisch","doi":"10.1007/JHEP02(2026)230","DOIUrl":"10.1007/JHEP02(2026)230","url":null,"abstract":"<p>We revisit the computation of the classical gravitational waveform for a particle moving in a plane wave background using on-shell amplitudes. We emphasize the relationship between gravitational memory and the boundary conditions of external scattering states, which were neglected in previous works. We then provide the first tree-level expression for the waveform that captures all memory effects. The waveform is presented in terms of Synge’s world function, with explicit tail terms, and a smooth weak memory limit. We also discuss the choice of BMS frame for the waveform on a plane wave background. In flat space, this corresponds to a choice of soft dressing of the initial state. We show that on a plane wave background, this dressing becomes a supertranslation of the waveform, in addition to a phase shift in the waveshape of the background.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)230.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341160","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 investigate the fate of the Standard Model (SM) ( {mathbb{Z}}_6^{(1)} ) electric 1-form global symmetry in the background of gravitational instantons, focusing on Eguchi-Hanson (EH) geometries. We show that EH instantons support quantized ( {mathbb{Z}}_6^{(1)} ) fluxes localized on their S2 bolt, inducing fractional topological charge without backreacting on the geometry. The requirement that quark and lepton wavefunctions be globally well-defined under parallel transport imposes boundary conditions, removing ill-defined fermion zero modes; the surviving spectrum is confirmed by an explicit solution of the Dirac equation and by the Atiyah-Patodi-Singer index theorem. The Euclidean path integral in the EH background can be interpreted as a transition amplitude from an entangled state between two identical halves of space to the vacuum. Summing over all ( {mathbb{Z}}_6^{(1)} ) flux sectors in the path integral gauges the SM 1-form symmetry; thus, it cannot persist as an exact global symmetry in the semiclassical limit of gravity. We further show that these fluxes induce baryon- and lepton-number violating processes, which are exponentially suppressed due to the smallness of the hypercharge coupling constant.
{"title":"Gauging the Standard Model 1-form symmetry via gravitational instantons","authors":"Mohamed M. Anber","doi":"10.1007/JHEP02(2026)225","DOIUrl":"10.1007/JHEP02(2026)225","url":null,"abstract":"<p>We investigate the fate of the Standard Model (SM) <span>( {mathbb{Z}}_6^{(1)} )</span> electric 1-form global symmetry in the background of gravitational instantons, focusing on Eguchi-Hanson (EH) geometries. We show that EH instantons support quantized <span>( {mathbb{Z}}_6^{(1)} )</span> fluxes localized on their <i>S</i><sup>2</sup> bolt, inducing fractional topological charge without backreacting on the geometry. The requirement that quark and lepton wavefunctions be globally well-defined under parallel transport imposes boundary conditions, removing ill-defined fermion zero modes; the surviving spectrum is confirmed by an explicit solution of the Dirac equation and by the Atiyah-Patodi-Singer index theorem. The Euclidean path integral in the EH background can be interpreted as a transition amplitude from an entangled state between two identical halves of space to the vacuum. Summing over all <span>( {mathbb{Z}}_6^{(1)} )</span> flux sectors in the path integral gauges the SM 1-form symmetry; thus, it cannot persist as an exact global symmetry in the semiclassical limit of gravity. We further show that these fluxes induce baryon- and lepton-number violating processes, which are exponentially suppressed due to the smallness of the hypercharge coupling constant.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)225.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341480","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}
Sergio Alameda-Calvo, Jose J. Blanco-Pillado, Alberto García Martín-Caro
The amplitude of an excited shape mode in a kink is expected to decay with a well-known power law via scalar radiation emission due to the nonlinear self-coupling of the scalar field. In this work we propose an alternative decay mechanism via pair production of fermions in a simple extension of the ϕ4 model in which the scalar field is coupled to a (quantum) fermionic field through a Yukawa-like interaction term. We study the power emitted through fermions as a function of the coupling constant in the semi-classical limit (without backreaction) and compare it to the case of purely scalar radiation emission.
{"title":"Quantum fermion emission from excited kinks","authors":"Sergio Alameda-Calvo, Jose J. Blanco-Pillado, Alberto García Martín-Caro","doi":"10.1007/JHEP02(2026)226","DOIUrl":"10.1007/JHEP02(2026)226","url":null,"abstract":"<p>The amplitude of an excited shape mode in a kink is expected to decay with a well-known power law via scalar radiation emission due to the nonlinear self-coupling of the scalar field. In this work we propose an alternative decay mechanism via pair production of fermions in a simple extension of the <i>ϕ</i><sup>4</sup> model in which the scalar field is coupled to a (quantum) fermionic field through a Yukawa-like interaction term. We study the power emitted through fermions as a function of the coupling constant in the semi-classical limit (without backreaction) and compare it to the case of purely scalar radiation emission.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)226.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341165","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 identify what has been referred to as ‘cut-off CFT’ in holographic braneworld with T2 or ( Toverline{T} ) theory (depending on the dimension of the bulk), so that the holographic dual of AdS-gravity with Neumann boundary conditions is a T2-deformed CFT that is set free. After making statements that apply for general dimensions higher than three, we focus on the case of a three-dimensional bulk. We find from bulk arguments that the effective theory on the brane is governed by a ( Toverline{T} )-like flow equation, such that under certain assumptions the effective gravity theory on the brane is given by a ( Toverline{T} )-like deformed timelike Liouville theory, which limits to the description of the holographic Weyl anomaly for branes that approach the asymptotic boundary.
{"title":"Setting T2 free for braneworld holography","authors":"Nele Callebaut, Matteo Selle","doi":"10.1007/JHEP02(2026)234","DOIUrl":"10.1007/JHEP02(2026)234","url":null,"abstract":"<p>We identify what has been referred to as ‘cut-off CFT’ in holographic braneworld with <i>T</i><sup>2</sup> or <span>( Toverline{T} )</span> theory (depending on the dimension of the bulk), so that the holographic dual of AdS-gravity with Neumann boundary conditions is a <i>T</i><sup>2</sup>-deformed CFT that is set free. After making statements that apply for general dimensions higher than three, we focus on the case of a three-dimensional bulk. We find from bulk arguments that the effective theory on the brane is governed by a <span>( Toverline{T} )</span>-like flow equation, such that under certain assumptions the effective gravity theory on the brane is given by a <span>( Toverline{T} )</span>-like deformed timelike Liouville theory, which limits to the description of the holographic Weyl anomaly for branes that approach the asymptotic boundary.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 2","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2026)234.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341164","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}