arXiv subjects

Song He

Publications and source records attributed to Song He.

At least 37 records · Page 2Linked to original sources

arXiv2026

Kinematics, cluster algebras and Feynman integrals

We identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of that for top-dimensional $G(4,n)$ corresponding to $n$-point massless kinematics. We provide evidence that they encode information about singularities of such Feynman integrals, including all-loop ladders with symbol letters given by cluster variables and algebraic generalizations. As a highly-nontrivial example, we apply $D_3$ cluster algebra to a $n=8$ three-loop wheel integral, which contains a new square root. Based on the $D_3$ alphabet and three new algebraic letters essentially dictated by the cluster algebra, we bootstrap its symbol, which is strongly constrained by the cluster adjacency. By sending a point to infinity, our results have implications for non-conformal Feynman integrals, e.g., up to two loops the alphabet of two-mass-easy kinematics is given by limit of this generalized $D_3$ alphabet. We also find that the reduction to three dimensions is achieved by folding and the resulting cluster algebras may encode singularities of amplitudes and Feynman integrals in ABJM theory, at least through $n=7$ and two loops.

hep-th↗

arXiv2026

Prospect on constraining environment-dependent dilaton model from gravitational redshift measurements

Scalar-tensor gravity represents a natural extension of general relativity. This paper investigates a conformal scalar-tensor gravity, the environmentally dependent dilaton model, and identifies regions of its parameter space potentially constrained by future experiments using atomic clocks to measure gravitational redshift. We propose an experimental scheme in which atomic clocks are placed in environments of different mass densities, such as ultrahigh vacuum, water, or osmium, and their frequency shifts are compared to probe the scalar field contribution to gravitational redshift. By further modeling the mass distribution in low-density environments with a discrete representation, we go beyond the standard continuous approximation. Despite limitations inherent to specific experimental configurations, our analysis reveals that a significant portion of the parameter space remains accessible. Importantly, the accessible regions are complementary to those constrained by existing tests, as they are primarily sensitive to relatively weak couplings. Consequently, high-precision gravitational redshift experiments hold the potential to exclude significant regions of this parameter space in the future.

gr-qc↗

arXiv2026

Leading singularities and chambers of Correlahedron

In this paper, we explore the chamber dissection of the loop-geometry of Correlahedron, which encodes the loop integrand of four-point stress-energy correlators in planar $\mathcal{N}=4$ super Yang-Mills. We demonstrate that at four loops, continuing the pattern of lower loops, the integrand of the four-point correlation function can be written as a sum over products of chamber-forms and local loop integrands. The chambers and their associated forms are identical to those of three loops, indicating that the dissection may be complete to all loop orders. Furthermore, this suggests that the leading singularities at all loops are simply linear combinations of these chamber forms. This is especially intriguing at four loops since it contains elliptic functions. Interestingly, each elliptic function appears in a subset of chambers. Our geometric approach motivates us to ``diagonalize" the representation, where the local integrals only possess a single leading singularity or elliptic cut. In such a representation, all integrands must evaluate to pure functions, including a single pure elliptic integrand. Inspired by this picture, we also present a simplified form of the three-loop correlator in terms of two independent pure functions (weight-$6$ single-valued multiple polylogarithms), which are directly computed from local integrands with unit leading singularities, multiplied by the leading singularities from chamber forms.

hep-th↗

arXiv2026

Loops and legs: ABJM amplitudes from $f$-graphs

We initiate a systematic study on how to extract planar integrands of (supersymmetric) scattering amplitudes with $L$ loops and $n$ legs in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the recently proposed (bosonic) generating function for squared amplitudes with $N:=n{+}L$ dual points; the latter enjoys a hidden permutation symmetry $S_N$ and is given by a linear combination of weight-$3$ planar $f$-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 ${\cal N}=4$ super Yang-Mills (SYM) from weight-$4$ $f$-graphs: we comment on this similarity and provide new results for $n=4$ ABJM loop integrand up to $L=6$. 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 $f$-graphs in $\mathcal{N}=4$ SYM.

hep-th↗

arXiv2026

On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods

We define and study infinite families of all-loop planar, dual conformal invariant (DCI) integrals, which contribute to four-point Coulomb-branch amplitudes and correlators in ${\cal N}=4$ supersymmetric Yang-Mills theory, by solving ``boxing'' differential equations via \texttt{HyperlogProcedures}~\cite{hyperlogprocedures}; The resulting single-valued harmonic polylogarithmic functions (SVHPL) are nicely labeled by ``binary'' strings of $0$ and $1$ without consecutive $1$'s. These functions are special cases of the so-called generalized ladders studied in~\cite{Drummond:2012bg}, where extended Steinmann relations (no consecutive $1$'s) are imposed due to planarity. Our results can be viewed as ``two-dimensional'' extensions of the well-known ladder integrals to many more infinite families of DCI integrals: the ladders have strings with a single $1$ followed by all $0$'s, and the other extreme, which nicely evaluate to the ``zigzag'' SVHPL functions with alternating $1$'s and $0$'s, are nothing but the four-point DCI integrals from the very special family of anti-prism $f$-graphs (while all other binary DCI integrals lie in between these two extreme cases). We also study periods of these integrals: while their periods are in general complicated single-valued multiple zeta values (SVMZV), the ``zigzag'' DCI integrals from anti-prism gives exactly the famous ``zigzag'' periods proportional to $ζ_{2L{+}1}$, and empirically it provides a numerical lower-bound for $L$-loop periods of any binary string, with the upper-bound given by that of the ladder (also proportional to $ζ_{2L{+}1}$). Based on $f$-graphs as a tool for studying these periods, we discuss several interesting facts and observations about these (motivic) SVMZV and relations among them to all loops, and enumerate a basis for them up to $L=10$.

hep-th↗

arXiv2026

A Unified Causal Framework for Nonlinear Electrodynamics Black Hole from Courant-Hilbert Approach: Thermodynamics and Singularity

We develop a unified framework for analyzing black hole thermodynamics and spacetime structure in Einstein gravity coupled to causal nonlinear electrodynamics (NED) in asymptotically anti-de Sitter backgrounds. The electromagnetic sector is governed by a Generalized Nonlinear Electrodynamics (GNED) Lagrangian obtained from a root-$T\bar T$ deformation constructed via the Courant-Hilbert approach, ensuring both duality invariance and causal propagation. This theory contains ModMax, Generalized Born-Infeld (GBI), 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.

hep-th↗

arXiv2026

Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations

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 $φ$-parity transformation. This classification is expressed through the structure of the irrelevant $T\bar{T}$-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: $φ$-parity-invariant, analytic theories are generated by irrelevant deformations built from integer powers of the energy-momentum tensor scalars, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m}({T_μ}^μ{T_ν}^ν)^{m}$. Conversely, $φ$-parity-violating, non-analytic theories require deformations involving both integer and half-integer powers, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m/2}({T_μ}^μ{T_ν}^ν)^{m/2}$. We prove this result in generality via a perturbative CH framework, showing that $φ$-parity invariance imposes specific constraints on the expansion coefficients of the CH function $\ell(τ)$ 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 $q=3/4$-deformed and "no $τ$-maximum" theories. Furthermore, we show how the $φ$-parity transformation is consistently generalized in the presence of a marginal root-$T\bar{T}$ coupling $γ$, and we derive the corresponding marginal and irrelevant flow equations for the studied theories.

hep-th↗

arXiv2026

Gravitational formulation of stress-tensor deformed field theories

Stress-tensor deformations suggest a geometric origin of emergent gravity but are typically non-local for $d>2$. We couple a seed QFT to Einstein gravity with deformation parameter $λ$ and evaluate the gravitational path integral at the metric saddle. Around a fixed reference background, the leading deformation is universal: a bilocal term quadratic in the stress tensor with kernel set by the graviton Green's function, plus a systematic higher-order expansion. Expressed on the saddle-point (deformed) metric, the flow becomes local. We then provide two constructive completions on deformed backgrounds--Palatini $f(R)$ gravity and an eigenvalue method for general Ricci-based theories--and apply them to scalar generalized Nambu-Goto and $\det T$ deformations (arbitrary $d$), two-dimensional multi-scalar ModMax and Born-Infeld models, and four-dimensional root-$T\bar T$ and $T\bar T$ flows of Maxwell theory yielding ModMax and Born-Infeld electrodynamics. In free field theory, an off-shell analysis further shows that the leading quantum correction generates an Einstein-Hilbert term with controlled higher-derivative terms.

hep-th↗

arXiv2026

Geometric realization of stress-tensor deformed field theory

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 $T\bar{T}$-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.

hep-th↗

arXiv2026

Self-Dual Electrodynamics via the Characteristic Method: Relativistic and Carrollian Perspectives

Electric-magnetic duality plays a pivotal role in understanding the structure of nonlinear electrodynamics (NED). The Gaillard-Zumino (GZ) criterion provides a powerful constraint for identifying self-dual theories. In this work, we systematically explore solutions to the GZ self-duality condition by applying the method of characteristics, a robust tool for solving nonlinear partial differential equations. Our approach enables the construction of new classes of Lagrangians that respect duality symmetry, both in the relativistic and Carrollian frameworks. In the relativistic setting, we not only recover well-known examples such as Born-Infeld and ModMax theories, but also identify novel models. We then generalize the GZ formalism to the Carrollian case and construct several classes of Carrollian self-dual non-linear electrodynamic models. Remarkably, we demonstrate that the characteristic flow exhibits an attractor behavior, in the sense that different seed theories that may not be self-dual can generate the same descendant self-dual Lagrangian. These findings broaden the landscape of self-dual theories and open new directions for exploring duality in ultra-relativistic regimes.

hep-th↗

arXiv2026

Hidden simplicity in AdS spinning Mellin amplitudes via scaffolding

We uncover surprising hidden simplicity in Mellin amplitudes for tree-level AdS holographic correlators for spinning operators, such as AdS "gluons" and "gravitons" (spin 1 and 2). We define Mellin amplitudes with $n$ spinning operators via the so-called "scaffolding" of $2n$-scalar ones with specific projection operators for each spin state, which are rational functions of Mellin variables of $2n$ scalars generalizing flat-space scaffolding amplitudes. We classify possible three-point structures with spin 1 and 2 which take the same form as massive three-point amplitudes in flat space, and match with special solutions such as those extracted from 6-scalar ones in $\mathrm{AdS}_5\times S^3$ or $\mathrm{AdS}_5\times S^5$. Focusing on $\mathrm{AdS}_5$ gluons, we directly bootstrap spinning amplitudes in scaffolding form up to $n=6$ gluons (which amounts to $2n=12$ scalars) using factorizations, multi-linearity and flat-space limit. The results take a remarkably simple form in analogy with flat-space amplitudes, which can be constructed from familiar 3- and 4-vertices as well as propagators of massive spin-1 particles. Surprisingly, we find that vertices with any descendant levels are proportional to the primary ones with nice combinatorial coefficients, which makes manifest the correct flat-space limit in the simplest possible way.

hep-th↗

arXiv2026

Neural Ordinary Differential Equations for Mapping the Magnetic QCD Phase Diagram via Holography

The QCD phase diagram is crucial for understanding strongly interacting matter under extreme conditions, with major implications for cosmology, neutron stars, and heavy-ion collisions. We present a novel holographic QCD model utilizing neural ordinary differential equations (ODEs) to map the QCD phase diagram under magnetic field $B$, baryon chemical potential $μ_B$, and temperature $T$. By solving the inverse problem of constructing a gravitational theory from Lattice QCD data, we reveal an unprecedentedly rich phase structure at finite $B$, including multiple critical endpoints (CEPs) in strong magnetic fields. Specifically, for {$B = 1.618 \, \mathrm{GeV}^2=2.592 \times 10^{19}$ Gauss}, we identify two distinct CEPs at $(T_C = 87.3 \, \mathrm{MeV}, \, μ_C = 115.9 \, \mathrm{MeV})$ and $(T_C = 78.9 \, \mathrm{MeV}, \, μ_C = 244.0 \, \mathrm{MeV})$. Notably, the critical exponents vary depending on the CEP's location, and the conventional scaling relations can be violated in the presence of strong magnetic fields. These findings significantly advance our understanding of the QCD phase structure and provide concrete predictions for experimental validation at upcoming facilities such as FAIR, JPARC-HI, and NICA.

hep-th↗

arXiv2025

Entanglement of General Subregions in Time-Dependent States

We develop a unified framework for computing Rényi and entanglement entropies of arbitrary spacetime intervals in time-dependent states of $(1+1)$-dimensional conformal field theories. By combining the spacetime density matrix formalism with the replica method, we show that entanglement entropy is well defined for both spacelike and timelike separations. Applying this framework to global quenches prepared by boundary states and to local quenches generated by operator insertions, we obtain analytic expressions for the entanglement entropy in general spacetime configurations. The results reveal qualitative differences between spacelike and timelike intervals: the timelike entanglement entropy is time-independent in the global quench model, depends solely on the temporal separation, and universally exhibits a constant imaginary contribution. These features are naturally explained by a generalized quasiparticle picture in which entanglement is produced precisely when one worldline of each quasiparticle pair intersects the interval. Furthermore, we demonstrate that the linear sum rule relating time- and spacelike entanglement persists in both global and local quenches, indicating a broader universality of spacetime entanglement in real-time quantum dynamics.

hep-th↗

arXiv2025

Relation between time- and spacelike entanglement entropy

In this study, we establish a connection between timelike 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 timelike and spacelike entanglement entropy, within which the imaginary component of timelike entanglement entropy can be understood as arising from the non-commutativity between the twist operator and its first-order temporal derivative.

hep-th↗

arXiv2025

Integrable Sigma Models and Universal Root $T\bar{T}$ Deformation via Courant-Hilbert Approach

We develop a unified Courant--Hilbert framework for constructing two-dimensional integrable sigma models deformed by two couplings: a marginal one $γ$ and an irrelevant one $λ$. The integrability condition is encoded in a nonlinear partial differential equation (PDE) for two invariants $(P_1, P_2)$, whose general solution could be expressed through an arbitrary generating function $\ell(τ)$. This formulation encompasses and extends known models, such as ModMax and Born-Infeld, while introducing new classes of solvable models with closed-form Lagrangians, including those with logarithmic and $q$-deformations. All resulting theories obey a universal root-$T\overline{T}$ flow equation, consistent under dimensional reduction from four-dimensional duality-invariant electrodynamics. Using perturbative expansions, we recover ModMax in the free limit, determine the $γ$-dependence of the coupling functions, and show how different flow equations, including a single-trace form, naturally emerge. Our results reveal deep structural connections between self-duality, integrability, and deformation dynamics across different dimensions.

hep-th↗

arXiv2025

Relative Rényi Entropy Under Local Quenches in 2D CFTs

We study the relative Rényi entropy (RRE) under local quenches in two-dimensional conformal field theories (CFTs), focusing on rational CFTs (RCFTs) and holographic CFTs. In RCFTs, the RRE evolves as a monotonic function over time, depending on finite-dimensional matrices. It is sometimes symmetric, prompting an exploration of its relation to the trace squared distance. We also observe that relative entropy can fail to distinguish between operators, as it only captures information entering/exiting the subsystem. In holographic CFTs, an analytic continuation of the RRE reveals insights into the entanglement wedge, offering a new perspective on bulk geometry in AdS/CFT. Our results deepen the understanding of quantum information measures in RCFTs and holographic CFTs, highlighting connections to distinguishability and bulk reconstruction.

hep-th↗

arXiv2025

Timelike Entanglement Entropy in Higher Curvature Gravity

This work investigates holographic timelike entanglement entropy in higher curvature gravity, with a particular focus on Lovelock theories and on the role of excited states. For strip subsystems, higher-curvature terms are found to affect the imaginary part of the entropy in a dimension-dependent manner, while excited states contribute solely to the real part. For the cases analyzed, spacelike and timelike entanglement entropies exhibit proportional relations: vacuum contributions differ by universal phase factors, while excitation contributions are linked by dimension-dependent rational coefficients. For hyperbolic subsystems, the timelike entanglement entropy computed via complex extremal surfaces is shown to agree with results obtained through analytic continuation, with imaginary contributions appearing in all dimensions. Higher-curvature corrections are explicitly calculated in five- and $(d+1)$-dimensional Gauss-Bonnet gravity, illustrating the applicability of the complex surface prescription to general Lovelock corrections. These results provide a controlled setting to examine the influence of higher-curvature interactions on holographic timelike entanglement entropy, and clarify its relation to vacuum and excited-state contributions.

hep-th↗

arXiv2025

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

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 result further reveal the dynamical connections between entanglement and gravity.

hep-th↗