arXiv subjects

Yanfeng Hang

Publications and source records attributed to Yanfeng Hang.

5 recordsLinked to original sources

arXiv2026

A Boolean-Lattice Perspective for All-Loop Two-Site Cosmological Wavefunction

We revisit the shifted-tree decomposition formula proposed in our previous work arXiv:2410.17192 for two-site cosmological wavefunction coefficients. For the two-site bubble-like family at arbitrary loop order, we show that the nontrivial central part of the decomposition reduces to an alternating subset sum over shifted diagonal divisors. This subset sum is naturally organized by the Boolean lattice associated with the internal energies, and can be rewritten as a product of commuting finite-difference operators acting on a seed divisor. The finite-difference form first gives a vertex expansion on the Boolean lattice and then leads to an equivalent maximal-chain expansion over complete filtrations from the empty subset to the full set of internal energies. We prove this maximal-chain formula in two complementary ways. Algebraically, the identity follows from a telescoping relation for products of shifted divisors. Geometrically, the finite-difference expression is represented by a cubical integral over the Boolean cube, while the maximal-chain expansion gives its simplex decomposition. After restoring the common two-site prefactor, this maximal-chain expansion reproduces the tubing representation of the loop-level wavefunction coefficient. Thus the shifted-tree decomposition and the tubing construction are two realizations of the same Boolean-lattice identity, providing a concrete geometric interpretation of the all-loop two-site formula.

hep-th↗

arXiv2026

Notes on Magnetic Monopoles from Partial Electromagnetic Duality

In this work, we propose a novel partial electromagnetic duality and construct its consistent realization using an extended gauge group $\mathrm{U}(1)_{\mathrm{q}}^{}\otimes\mathrm{U}(1)_{\mathrm{d}}^{}$ over a localized space region, where $\mathrm{U}(1)_{\mathrm{q}}^{}$ is the conventional gauge group of QED and $\mathrm{U}(1)_{\mathrm{d}}^{}$ serves as its dual gauge group. In this framework, the "electric" charge associated with $\mathrm{U}(1)_{\mathrm{d}}^{}$ plays the role of the magnetic (monopole) charge in QED $\mathrm{U}(1)_{\mathrm{q}}^{}$, whereas the electric charge of $\mathrm{U}(1)_{\mathrm{q}}^{}$ is reinterpreted as the "magnetic" charge of $\mathrm{U}(1)_{\mathrm{d}}^{}$. Importantly, our theory preserves the exact Bianchi identity, as it provides a genuinely singularity-free and stringless formulation that involves only electric charges under each U(1) gauge group. We show that the two gauge sectors, $\mathrm{U}(1)_{\mathrm{q}}^{}$ and $\mathrm{U}(1)_{\mathrm{d}}^{}$, exhibit a partial duality within a localized region of space. Based on this consistent formulation, we present the first fully gauge-invariant computation of scattering amplitudes and cross sections for monopole production processes, including $\mathrm{e}^-\mathrm{e}^+\rightarrow\chi\chi^*$ and $\mathrm{e}^-\mathrm{e}^+\rightarrow\chi\bar{\chi}$.

hep-ph↗

arXiv2025

Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions

We investigate the scattering amplitudes of massive Kaluza-Klein (KK) states in compactified five-dimensional warped gauge and gravity theories. Focusing on tree-level $2\to2$ processes, we analyze the leading-order amplitudes involving bulk KK matter fields and KK gauge/gravitational Goldstone bosons. By imposing the gauge theory equivalence theorem (GAET) and the gravitational equivalence theorem (GRET) within warped KK theories, we systematically reconstruct the leading-order amplitudes for physical KK gauge bosons and gravitons, thereby circumventing the intricate energy cancellations inherent in physical amplitudes. Within this framework, the correspondence between GAET and GRET arises as a direct manifestation of the leading-order double-copy relation in the high-energy expansion. This connection provides a foundation for extending the BCJ double-copy construction to four-point amplitudes involving bulk KK matter fields, and further generalizes to arbitrary $N$-point cases, enabling a systematic derivation of the corresponding gravitational amplitudes with consistent incorporation of KK matter fields at leading order.

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arXiv2024

A Note on Kinematic Flow and Differential Equations for Two-Site One-Loop Graph in FRW Spacetime

In this work, we systematically study the differential systems governing loop-level wavefunction coefficients of conformally-coupled scalar field theory within a general power-law FRW cosmology. By utilizing the twisted cohomology, hyperplane arrangements, and IBP techniques, we derive the canonical differential equations for two-site one-loop bubble and tadpole systems, revealing distinct structural differences. We present new insights into the one-loop tadpole system, uncovering that its integral family can include multiple parent functions due to distinct pairs of relative hyperplane associated with each function, unlike the single parent function appearing in the one-loop bubble case. Moreover, we demonstrate that the tadpole correlator selectively probes only a subset of the cohomology space, despite the hyperplane arrangement suggesting a higher-dimensional structure. Another novel contribution of this work is the extension of kinematic flow framework to the loop-level scenarios for the first time. Using a graphical approach based on family trees generated by marked tubing graphs, which encode singularity structures, we efficiently construct the differential equations and uncover the hierarchical relationships among the associated master integrals. Additionally, we provide a preliminary discussion on generalization to two-site higher-loop configurations. We propose a general decomposition formula for the canonical form of a two-site diagram with arbitrary loops, breaking it into unshifted and shifted components associated with the fundamental tree-level and bubble-like structures, and establish a block-wise decomposition rule for the matrix $\tilde{A}$ in the corresponding differential system. These advancements provide a unified framework for two-site loop-level correlators and lay the groundwork for future study of more complex multi-site loop systems.

hep-th↗

arXiv2024

Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space

We study the structure of scattering amplitudes of massive Kaluza-Klein (KK) states in the compactified 5-dimensional warped gauge and gravity theories. We present systematic formulations of the gauge theory equivalence theorem (GAET) and the gravitational equivalence theorem (GRET) for warped KK theories in $R_\xi^{}$ gauge, where the GAET connects the scattering amplitudes of longitudinal KK gauge bosons to that of the corresponding KK Goldstone bosons and the GRET connects the scattering amplitudes of KK gravitons of helicity-zero (helicity-one) to that of the corresponding gravitational scalar (vector) KK Goldstone bosons. We analyze the structure of 3-point and 4-point scattering amplitudes of massive KK gauge bosons and of massive KK gravitons as well as their corresponding Goldstone bosons. We first prove the GAET and GRET explicitly for the fundamental 3-point KK gauge/gravity scattering amplitudes. We then demonstrate that the validity of the GAET and GRET for 4-point gauge/gravity scattering amplitudes can be reduced to the validity of GAET and GRET for 3-point gauge/gravity scattering amplitudes at tree level. With these, we study the double-copy construction of KK scattering amplitudes in the warped gauge/gravity theories. We newly realize the double-copy for massive 3-point full gauge/gravity amplitudes at tree level under proper correspondences of color-kinematics and of gauge/gravity couplings, whereas we can construct the double-copy for 4-point KK gauge/gravity amplitudes to the leading order (LO) of high energy expansion. We also conjecture that this LO double-copy construction can be extended to $N$-point scattering amplitudes with $N\!\geqslant 5$.

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