We present a single, dimension-independent framework that links four-dimensional duality-invariant nonlinear electrodynamics to two-dimensional integrable sigma models. Both sectors are shown to obey the same firs-order Courant–Hilbert equation, solved by a common generating function and an auxiliary-potential formulation. Within this structure, a discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>φ</mi></math> parity acts as a selection rule, organizing deformation series into integer versus fractional powers. Two commuting deformations—an irrelevant parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> and a marginal parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>—admit universal flow representations that recover 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> dynamics and extend them in a controlled way. The construction yields closed-form families (generalized Born-Infeld, logarithmic, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> deformed) and a new integrable model, all realized in 2D and 4D. These results replace case-by-case analyses with a unified route to solvable nonlinear theories, with immediate relevance to gauge dynamics, string-inspired effective actions, and integrable models.

China

H. Babaei-Aghbolagh

Bin Chen

Germany

Song He

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> flows unify 4D duality-invariant electrodynamics and 2D integrable sigma models

We define the “squared amplitudes” in planar Aharony-Bergman-Jafferis-Maldacena theory, analogous to those in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> super-Yang-Mills (SYM) theory. Surprisingly, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math>-point <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>-loop integrands with fixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≔</mo><mi>n</mi><mo>+</mo><mi>L</mi></mrow></math> are unified in a single generating function. Similar to the SYM four-point half–Bogomol’nyi-Prasad-Sommerfield correlator integrand, the generating function enjoys a hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>N</mi></msub></math> permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs. Remarkably, through Gram identities it can also be represented as a linear combination of “bipartite” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs that manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>4</mn></math>, 6, 8. By drawing analogies with SYM, we conjecture some “graphical rules” the generating function satisfies, and exploit them to bootstrap a unique <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>10</mn></math> result, which provides new results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>10</mn></math> squared tree amplitudes, as well as integrands for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>L</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo stretchy="false">)</mo><mo>,</mo><mo stretchy="false">(</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo stretchy="false">)</mo></mrow></math>. Our results strongly suggest the existence of a “bipartite correlator” in Aharony-Bergman-Jafferis-Maldacena theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.

Canxin Shi

Yichao Tang

Yao-Qi Zhang

Hidden Permutation Symmetry of Squared Amplitudes in Aharony-Bergman-Jafferis-Maldacena Theory

The experimentally observed temperature-dependent shear and bulk viscosities of the quark-gluon plasma (QGP), along with its apparent violation of the Kovtun-Son-Starinets (KSS) bound $\textit{η}$/$\textit{s}$ = 1/(4$\textit{π}$), necessitate a holographic description that incorporates higher-derivative corrections. We propose a five-dimensional Einstein-Scalar-Maxwell-Gauss-Bonnet model in which a scalar-Gauss-Bonnet coupling $\textit{H}$($\textit{ϕ}$) encodes leading curvature corrections. Although no closed-form black hole solution is available, we employ an entropy-production analysis at the event horizon to derive exact analytic formulas for the shear viscosity $\textit{η}$ and bulk viscosity $\textit{ζ}$. These expressions exhibit apparent deviation from the KSS bound and nontrivial temperature dependence. We then perform an independent computation via the retarded Green function (Kubo) method, finding perfect agreement for $\textit{η}$ and isolating a single constant in $\textit{ζ}$ that requires numerical determination. Our dual derivation underscores the pivotal role of higher-derivative terms in realistic QGP modeling and demonstrates the efficacy of nonanalytic holographic backgrounds in capturing the dynamics of strongly coupled fluids.

Chenwei Tong

India

Rohit Mishra

Yanqi Wang

Hydrodynamical transports in generic AdS Gauss-Bonnet-scalar gravity

We revisit the conjectural method called Schubert analysis for generating the alphabet of symbol letters for Feynman integrals, which was based on geometries of intersecting lines associated with corresponding cut diagrams. We explain the effectiveness of this somewhat mysterious method by relating such geometries to the corresponding Landau singularities, which also amounts to “uplifting” Landau singularities of a Feynman integral to its symbol letters. We illustrate this $\textit{Landau-based Schubert analysis}$ using various multi-loop Feynman integrals in four dimensions and present an automated Mathematica notebook for it. We then apply the method to a simplified problem of studying alphabets of physical quantities such as scattering amplitudes and form factors in planar $$ \mathcal{N} $$ = 4 super-Yang-Mills. By focusing on a small set of Landau diagrams (as opposed to all relevant Feynman integrals), we show how this method nicely produces the two-loop alphabet of $\textit{n}$-point MHV amplitudes and that of the $\textit{n}$ = 4 MHV form factors. A byproduct of our analysis is an explicit representation of any symbol alphabet obtained this way as the union of various type-$\textit{A}$ cluster algebras.

Xuhang Jiang

Jiahao Liu

Qinglin Yang

Landau-based Schubert analysis

In this study, we establish a connection between time- and spacelike entanglement entropy. We show that timelike entanglement entropy is closely related to spacelike entanglement entropy and its temporal derivative. For a broad class of states, it can be uniquely determined by a linear combination of spacelike entanglement entropy and its first-order temporal derivative. This relation holds, for instance, in states conformally equivalent to the vacuum in two-dimensional conformal field theories. For more general states, we demonstrate that the relation can be constructed perturbatively. Our results suggest that timelike entanglement entropy is constrained by causality. Moreover, this relation provides a unified framework for time- and spacelike entanglement entropy, within which the imaginary component of timelike entanglement entropy can be understood as arising from the noncommutativity between the twist operator and its first-order temporal derivative.

Wu-zhong Guo

Yu-Xuan Zhang

Relation between time- and spacelike entanglement entropy

We study multiloop conformal integrals for four-point correlators of planar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super-Yang-Mills theory, and in particular those contributing to Coulomb branch amplitudes in the ten-dimensional lightlike limit, where linear combinations of such integrals are determined by the large R-charge octagons exactly known from integrability. Exploiting known results for integrands, we review those combinations of dual conformal invariant (DCI) integrals that must evaluate to determinants of ladders, generalizing the simplest cases of Basso-Dixon fishnet integrals; in this way, we summarize all-loop predictions for the integrands (which are extracted from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math>-graphs) contributing to components of Coulomb branch amplitudes, such as next-to-fishnet integrals. Moreover, this exercise produces new “magic identities,” i.e., certain combinations of DCI integrals equal zero, and we enumerate and simplify such identities up to six loops explicitly. On the other hand, most of these individual integrals have not been computed beyond three loops, and as a first step we consider a bootstrap program for DCI integrals based on their leading singularities and the space of pure functions. We bootstrap the 3 nontrivial DCI integrals for four-loop Coulomb branch amplitudes (providing an independent verification of the four-loop magic identity), which all take remarkably simple form as weight-8 single-valued harmonic polylogarithms. We also compute all leading singularities and a large portion of the pure functions for the 34 DCI integrals contributing to five-loop amplitudes, where not only some integrals evaluate to functions beyond harmonic polylogarithms, but they also contain lower-weight pieces individually.

Notes on conformal integrals: Coulomb branch amplitudes, magic identities, and bootstrap

We present a model-independent extraction of the $$\phi $$ – $$^{4}\textrm{He}$$ scattering length from near-threshold $$\phi $$ photoproduction on helium-4, based on LEPS Collaboration data for the coherent process $$\gamma + {}^{4}\textrm{He} \rightarrow \phi + {}^{4}\textrm{He}$$ and the Vector Meson Dominance framework. Assuming an energy-independent differential cross section, we extract the absolute value of the $$\phi -^4\!\textrm{He}$$ scattering length $$|\alpha _{\phi ^{4}\textrm{He}}| = (3.33 \pm 0.06) \times 10^{-4}~\textrm{fm}$$ from a fit at threshold $$t_{\text {thr}}$$ . This value is orders of magnitude smaller than those for $$\phi N$$ and $$\phi d$$ scattering length, indicating an inverse dependence of $$|\alpha _{VA}|$$ on the target nucleus mass. Our results provide new insight into the $$\phi $$ –nucleus interaction, supporting the notion of weak $$\phi $$ –nucleus coupling. We further explore the dependence of $$|\alpha _{VA}|$$ on the vector meson mass, the target atom mass, and the threshold energy. An approximate exponential suppression of $$|\alpha _{VA}|$$ is observed with increasing vector meson mass or target atom mass, indicating that heavier vector mesons or heavier target nuclei exhibit weaker couplings in vector meson–nucleus interactions.

Chengdong Han

Wei Kou

Rong Wang

Xurong Chen

First extraction of the $$\phi $$ - $$^{4}\textrm{He}$$ scattering length from near-threshold $$\phi $$ photoproduction on helium-4

We demonstrate that the necessary condition for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation, corresponds precisely to the integrability condition. We derive a general perturbation solution to this partial differential equation, which includes both 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> flow equation and an irrelevant <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 flow equation. Additionally, we identify a general form for these flow equations that commute with each other. Our results establish a general integrable theory characterized by theory-dependent coefficients at each order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> expansion. This unified framework systematically classifies all integrable theories possessing two Lorentz-invariant variables (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math>) while accommodating arbitrary orders of the coupling constants (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>). The theory provides a comprehensive classification scheme that encompasses both known and novel integrable systems within this class.

Hao Ouyang

Generalized <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 flows for scalar theories in two dimensions

We holographically study the far-from-equilibrium isotropization dynamics of the strongly coupled $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills plasma. The dual gravitational background is driven to be out of equilibrium and anisotropic by a time-dependent change in boundary conditions. At late times, the system relaxes and asymptotically approaches a static configuration. The large initial energy densities accelerate the isotropization significantly compared to the initial geometry corresponding to the supersymmetric Yang-Mills vacuum. We analyze shear transport during isotropization by directly computing the time-dependent stress tensor, which is now a nonlinear function of the shear rate. The shear viscosity far from equilibrium displays much richer dynamics than its near-equilibrium counterpart. Moreover, we uncover that the equilibrium viscosity-to-entropy ratio at late times depends on the details of the quench function and the initial data, which could be due to a resummation of the hydrodynamic description. In particular, this ratio can be parametrically smaller than the Kovtun-Son-Starinets bound calculated from linear response theory.

Shoucheng Wang

Li Li

Shear transport in far-from-equilibrium isotropization of supersymmetric Yang-Mills plasma

The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an auxiliary field, $\textit{τ}$, and Courant-Hilbert functions, $\textit{ℓ}$($\textit{τ}$), which depend on $\textit{τ}$. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions $$ \frac{\partial \ell }{\partial \tau}\ge 1 $$ and $$ \frac{\partial^2\ell }{\partial {\tau}^2}\ge 0 $$ .