We extend the entanglement first law of conformal field theory (CFT) to timelike subregions. Focusing on intervals along the time direction of the boundary CFT, we show that the associated timelike entanglement entropy obeys a first-law-like relation, with an effective entanglement temperature inversely proportional to the temporal size of the interval. By implementing a double Wick rotation, we obtain the exact modular Hamiltonian for a suitable hyperbolic subsystem and use it to formulate the timelike entanglement first law precisely. Our central result is a detailed proof that, in asymptotically Anti-de Sitter spacetime, this timelike entanglement first law is equivalent to linearized Einstein’s equations in the bulk: the first law follows from the linearized equations and, conversely, implies them. Our results further reveal the dynamical connections between entanglement and gravity.

China

Guo-Ying Li

Mei-Hui Xiao

Song He

Jia-Rui Sun

Entanglement first law for timelike entanglement entropy and linearized Einstein’s equation

In this work, we extend the impulse approximation for the generalized parton distributions (GPDs) of a spin-0 composite hadron with spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> constituents to manifestly incorporate the symmetries of the target wave function. The method utilizes a light-front Wigner function representation instead of a spectral density and a basis of Pauli matrices for the spin. It exploits the boost invariance of the light front and rotational invariance in the rest frame to parametrize the Wigner density in terms of only 3 structures. In addition to the isotropic term and a term describing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>L</mi><mo stretchy="false">→</mo></mover><mo>·</mo><mover accent="true"><mi>S</mi><mo stretchy="false">→</mo></mover></math> coupling previously observed for transverse momentum dependent parton distributions (TMDs), we also identify a novel coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mover accent="true"><mi>L</mi><mo stretchy="false">→</mo></mover><mo>·</mo><mover accent="true"><mi>S</mi><mo stretchy="false">→</mo></mover></math> to the angular momentum transfer which is unique to the case of GPDs. We then apply the framework to a composite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></math> target with simple phenomenological models to identify qualitative experimental signatures of composite-structure effects in light nuclei. The framework we have constructed here can be readily extended to the case of generalized TMDs (GTMDs), while the phenomenological framework is applicable both to analyses of light nucleus data and as training input for AI-assisted applications.

United States

Antonio Garcia Vallejo

Matthew D. Sievert

Probing composite structure and spin-orbit coupling with GPDs in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></math>

We identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of cluster algebras for Grassmannian $\textit{G}$(4, $\textit{n}$) corresponding to $\textit{n}$-point massless kinematics. We classify such algebras for cases through eight points, and provide evidence that singularities of the corresponding Feynman integrals are given by cluster variables and their algebraic generalizations. By sending a point to infinity, our results have implications for symbology of non-conformal Feynman integrals. We also find that dimensional reduction is achieved by $\textit{folding}$ and the resulting cluster algebras encode singularities of Feynman integrals in three dimensions. As a highly-nontrivial application, we study a eight-point three-loop wheel integral whose kinematics correspond to two-mass-easy box in the non-conformal limit: in addition to nine rational letters that are cluster variables, we also find three algebraic letters containing a new square root, in accordance with results from differential equations for two-loop case. Based on this alphabet, we bootstrap its symbol, which turns out to be strongly constrained by cluster adjacency conditions.

Zhenjie Li

Qinglin Yang

Kinematics, cluster algebras and Feynman integrals

We initiate a systematic study on how to extract planar integrands of (supersymmetric) scattering amplitudes with $\textit{L}$ loops and $\textit{n}$ legs in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the recently proposed (bosonic) generating function for squared amplitudes with $\textit{N}$ := $\textit{n}$+$\textit{L}$ dual points; the latter enjoys a hidden permutation symmetry $\textit{S}$ and is given by a linear combination of weight-3 planar $\textit{f}$ -graphs that can be recast as bipartite graphs, which manifest important properties of ABJM amplitudes. We provide evidence that it contains sufficient information to reconstruct individual amplitudes, despite the absence of squared amplitudes at odd loops. The extraction of the four-point amplitude is already non-trivial and closely parallels the extraction of five-point amplitudes in $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM) from weight-4 $\textit{f}$-graphs: we comment on this similarity and provide new results for $\textit{n}$ = 4 ABJM loop integrand up to $\textit{L}$ = 6. For higher multiplicities, based on Yangian invariants (including BCFW building blocks for tree amplitudes) and an appropriate basis of planar dual conformal invariant(DCI) integrands, we disentangle six-point integrands up to two loops and eight-point tree amplitude from the squared amplitudes. Our results suggest that ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes, closely paralleling the role of $\textit{f}$-graphs in $$ \mathcal{N} $$ = 4 SYM.

United Kingdom

Yao-Qi Zhang

Loops and legs: ABJM amplitudes from $\textit{f}$-graphs

In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

We investigate the classification of self-dual nonlinear electrodynamic (NED) theories based on their analyticity properties, which are directly linked to invariance under a discrete $\textit{φ}$-parity transformation. This classification is expressed through the structure of the irrelevant $$ T\overline{T} $$ -like deformations that generate the theories from a Maxwell seed. Using both closed-form and perturbative methods within the Courant-Hilbert (CH) and Russo-Townsend auxiliary field formalisms, we demonstrate a precise correspondence: $\textit{φ}$-parity-invariant, analytic theories are generated by irrelevant deformations built from integer powers of the energy-momentum tensor scalars, $$ {\mathcal{O}}_{\lambda } $$ ~ Σ $\textit{C}$ ($\textit{T}$ $\textit{T}$ ) ($\textit{T}$ $\textit{T}$ ) . Conversely, $\textit{φ}$-parity-violating, non-analytic theories require deformations involving both integer and half-integer powers, $$ {\mathcal{O}}_{\lambda } $$ ~ Σ $\textit{C}$ ($\textit{T}$ $\textit{T}$ ) ($\textit{T}$ $\textit{T}$ ) . We prove this result in generality via a perturbative CH framework, showing that $\textit{φ}$-parity invariance imposes specific constraints on the expansion coefficients of the CH function $\textit{ℓ}$($\textit{τ}$) which, in turn, force all half-integer powers in the deformation to vanish. The classification is explicitly verified for known closed-form theories: the analytic generalized Born-Infeld model and the non-analytic examples of the $\textit{q}$ = 3/4-deformed and “no $\textit{τ}$-maximum” theories. Furthermore, we show how the $\textit{φ}$-parity transformation is consistently generalized in the presence of a marginal root- $$ T\overline{T} $$ coupling $\textit{γ}$, and we derive the corresponding marginal and irrelevant flow equations for the studied theories.

Iran

H. Babaei-Aghbolagh

Komeil Velni

Germany

Zahra Pezhman

Classifying causal nonlinear electrodynamics via $\textit{φ}$-parity and irrelevant deformations

Motivated by recent HAL QCD simulations of the <italic>&#981;N</italic> interaction in the 4 <italic>S</italic> <inf>3/2</inf> channel and its modification in the 2 <italic>S</italic> <inf>1/2</inf> channel, we develop a first-principles few-body framework that embeds these potentials into configuration-space Faddeev&#8211;Yakubovsky equations. We predict bound <math altimg='si30.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup><mi mathvariant='normal'>H</mi></mrow></math>, <math altimg='si31.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup><mtext>He</mtext></mrow></math>, and <math altimg='si32.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>5</mn></msubsup><mtext>He</mtext></mrow></math> nuclei by performing calculations for <italic>&#981;</italic>-mesic <italic>&#981;NNN</italic> and <italic>&#981;NNNN</italic> systems. Both spin-dependent and spin-independent <italic>&#981;N</italic> interactions are considered, leading to deeply and moderately bound states, respectively. The deeply bound states originate from the strong attraction in the 2 <italic>S</italic> <inf>1/2</inf> <italic>&#981;N</italic> channel. Coulomb shifts of the binding energies are evaluated. Our findings provide the binding mechanism and demonstrate the importance of short-range <italic>&#981;N</italic> attraction.

France

R. Lazauskas

R.Ya. Kezerashvili

I. Filikhin

Possible existence of <math altimg='si22.svg'><msubsup><mrow /><mi>&#981;</mi><mn>3</mn></msubsup></math>H, <math altimg='si23.svg'><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup></math>H, <math altimg='si23.svg'><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup></math>He, and <math altimg='si24.svg'><msubsup><mrow /><mi>&#981;</mi><mn>5</mn></msubsup></math>He nuclei

We develop a unified framework for analyzing black hole thermodynamics and spacetime structure in Einstein gravity coupled to causal nonlinear electrodynamics in asymptotically anti–de Sitter (AdS) backgrounds. The electromagnetic sector is governed by a generalized nonlinear electrodynamics Lagrangian obtained from a root-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math> deformation constructed via the Courant-Hilbert approach, ensuring both duality invariance and causal propagation. This theory contains modified Maxwell (ModMax), generalized Born-Infeld, and self-dual logarithmic electrodynamics as continuous limits. Within this framework we obtain exact charged AdS black hole solutions and perform a detailed study of their thermodynamic properties, including mass, temperature, entropy, and free energy. The resulting phase structure exhibits van der Waals–type transitions between small and large black holes and features a characteristic swallowtail in the free energy at the critical point. We further investigate the internal geometry, showing that the nature of the central singularity is determined by the matter fields that source the spacetime. An analysis of the Kretschmann scalar reveals how mass and electric charge jointly govern curvature divergence in ModMax black holes. We derive an explicit charge-to-mass bound within a causal logarithmic electrodynamic theory. This extends the finite self-energy property of the point charge beyond the standard Born-Infeld model. This bound cleanly distinguishes black holes from naked singularities, showing that naked singularities occur precisely when the mass parameter is smaller than the electromagnetic self-energy of the point charge. This provides a clear energetic criterion for horizon formation in the absence of a Cauchy horizon.

Komeil Babaei Velni

Fateme Isapour

Unified causal framework for a nonlinear electrodynamics black hole from the Courant-Hilbert approach: Thermodynamics and singularity

We present a semiclassical framework in which stress-tensor deformations of a quantum field theory (QFT) reorganize into a gravitational action evaluated at a metric saddle. The deformed partition function can be written as a gravitational path integral evaluated at the saddle, establishing a direct link between stress-tensor flows and gravitational dynamics. Two complementary routes arise: (i) from gravitational actions such as Einstein and Palatini, which map to stress-tensor deformations of a seed QFT; and (ii) from deformed QFTs such as generalized Nambu-Goto and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-like deformed models, which reconstruct the corresponding gravitational actions. Finally, in a free, massive scalar theory, we show that the one-loop effective action of the nonlocal deformation contains a local curvature term; its coefficient defines an induced Newton constant at a chosen renormalization scale, thereby demonstrating a bidirectional link between stress-tensor flows and classical gravity.

Yun-Ze Li

Yunfei Xie

Geometric realization of stress-tensor deformed field theory

We report an experimental investigation of an unexplored breakup pathway of 6Li proceeding via one-proton stripping to the unbound 5He nucleus, followed by its decay into <math altimg='si22.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>+</mo><mi>n</mi></mrow></math>, in the 6Li + 112Sn reaction at <math altimg='si3.svg'><mrow><msub><mi>E</mi><mrow><mrow><mi mathvariant='normal'>b</mi></mrow><mi>e</mi><mi>a</mi><mi>m</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>30</mn></mrow></math> MeV. Coincident <italic>&#945;</italic>- <italic>n</italic> events were measured using an array of silicon strip telescopes in conjunction with liquid scintillator neutron detectors. Successive kinematical cuts on the reconstructed projectile-like, fragment energies and Q-values enabled a clear separation of contributions arising purely through 5He <math altimg='si6.svg'><mrow><mo>&#8594;</mo><mi>&#945;</mi><mo linebreak='goodbreak'>+</mo><mi>n</mi></mrow></math> from competing processes such as evaporation following complete and incomplete fusion. The resultant relative energy distributions exhibit a pronounced peak at 0.84 MeV, indicating sequential breakup through the first unbound resonance 5He(3/2 <math altimg='si23.svg'><msup><mrow /><mo>&#8722;</mo></msup></math>) and show good agreement with Monte-Carlo simulations. Absolute breakup cross-sections for the ( 6Li, 5He&#8239;&#8594;&#8239; <italic>&#945;n</italic>) channel are determined using the efficiency-corrected yields. In addition, angular distributions for elastic scattering and breakup cross sections are interpreted within coupled-channels (CDCC+CRC) framework. The present results provide valuable insight into transfer-induced breakup dynamics of weakly bound nuclei near the Coulomb barrier.

India

Tanya Singh

S. Santra

P.C. Rout

A. Pal

A. Baishya

H. Kumawat

T. Santhosh

M. Meher

Jyotisankar Das

Ramandeep Gandhi

Sequential breakup of 6Li via ( 6Li, 5He <math altimg='si6.svg'><mrow><mo>&#8594;</mo><mi>&#945;</mi><mo linebreak='goodbreak'>+</mo><mi>n</mi></mrow></math>) reaction