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Canxin Shi

Publications and source records attributed to Canxin Shi.

17 recordsLinked to original sources
arXiv2026

Classical dynamics from QFT via Stratonovich-Weyl correspondence

We develop a formalism for extracting relativistic classical dynamics from the S-matrix, in which massive bodies are described on phase space while massless radiation is kept in the Fock space. Our formalism relies on the Stratonovich-Weyl (SW) correspondence between the operator and phase-space formulations of quantum mechanics, as implemented covariantly by the SW quantizer. For localized incoming states, classical observables are given by SW symbols of the appropriate operators evaluated on incoming asymptotic trajectories. In combination with the exponential form of the S-matrix, the observables are naturally given by nested mixed Dirac/commutator brackets involving Magnus amplitudes. The latter are the matrix elements of the logarithm of the S-matrix, and we provide a straightforward algorithm for computing the combinatorial Murua coefficients that control the placement of retarded propagators inside Magnus-amplitude diagrams. This picture is well-suited for gravitational-wave physics applications.

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arXiv2026

Bootstrapping Giant Graviton Correlators

We develop bootstrap methods for mixed heavy-light four-point correlators $\langle GGOO\rangle$ in $\mathcal N=4$ super-Yang--Mills theory at large $N$, where $O\equiv {\cal O}_2$ is the chiral primary operator in the stress-tensor multiplet and $G$ are (dual) giant graviton operators with dimension of order $N$, including the maximal determinant case. The loop integrand is expanded in a basis of labelled $f$-graphs -- necessarily including non-planar topologies due to the dimension-$N$ nature of the giant gravitons -- and the coefficients are fixed by various bootstrap conditions including double-triangle and triangle rules in the cusp and OPE limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries $\mathcal{O}_k$. Together, these inputs uniquely determine the correlator through three loops, passing further non-trivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.

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arXiv2025

A Hidden Permutation Symmetry of Squared Amplitudes in ABJM Theory

We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in $\mathcal{N}{=}4$ super-Yang-Mills theory (SYM). Surprisingly, the $n$-point $L$-loop integrands with fixed $N{:=}n{+}L$ are unified in a single generating function. Similar to the SYM four-point half-BPS correlator integrand, the generating function enjoys a hidden $S_N$ permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar $f$-graphs. Remarkably, through Gram identities it can also be represented as a linear combination of bipartite $f$-graphs which 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 $n$ with $N{=}4,6,8$. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique $N{=}10$ result, which provides new results for $n{=}10$ squared tree amplitudes, as well as integrands for $(n,L){=}(4,6),(6,4)$. Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.

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arXiv2025

Dirac brackets for classical radiative observables

We introduce a new coherent state expansion of the exponential representation of the S-matrix for the classical gravitational two-body problem. By combining the Kosower-Maybee-O'Connell (KMOC) formalism with the Dirac bracket structure emerging in the classical limit, we derive compact and gauge-invariant expressions for scattering observables in the presence of radiation. This causal formulation bypasses the calculation of KMOC cuts and provides a direct link between observables and a minimal set of classical matrix elements extracted from amplitudes. We illustrate our method with several examples, including the impulse, spin kick, angular momentum, waveform and the related radiative fluxes. Finally, using our formalism we evaluate for the first time the spin kick and the change in angular momentum of each particle up to $\mathcal{O}(G^2 s_1^{j_1} s_2^{j_2})$ with $j_1+ j_2 \leq 11$.

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arXiv2025

The Four-Point Correlator of Planar sYM at Twelve Loops

We determine the 4-point correlation function and amplitude in planar, maximally supersymmetric Yang-Mills theory to 12 loops. We find that the recently-introduced 'double-triangle' rule in fact implies the previously described square and pentagon rules; and when applied to 12 loops, it fully determines the 11-loop correlator and fixes all but 3 of the (22,024,902) 12-loop coefficients; these remaining coefficients can be subsequently fixed using the '(single-)triangle' rule. Not only do we confirm the Catalan conjecture for anti-prism graphs, but we discover evidence for a greatly generalized Catalan conjecture for the coefficients of all polygon-framed fishnet graphs. We provide all contributions through 12 loops as ancillary files to this work.

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arXiv2024

The Cusp Limit of Correlators and A New Graphical Bootstrap for Correlators/Amplitudes to Eleven Loops

We consider the universal behavior of half-BPS correlators in $\mathcal{N}=4$ super-Yang-Mills in the cusp limit where two consecutive separations $x_{12}^2,x_{23}^2$ become lightlike. Through the Lagrangian insertion procedure, the Sudakov double-logarithmic divergence of the $n$-point correlator is related to the $(n+1)$-point correlator where the inserted Lagrangian "pinches" to the soft-collinear region of the cusp. We formulate this constraint as a new graphical rulefor the $f$-graphs of the four-point correlator, which turns out to be the most constraining rule known so far. By exploiting this single graphical rule, we bootstrap the planar integrand of the four-point correlator up to ten loops ($n=14$) and fix all 22024902 but one coefficient at eleven loops ($n=15$); the remaining coefficient is then fixed using the triangle rule. We verify the "Catalan conjecture" for the coefficients of the family of $f$-graphs known as "anti-prisms" where the coefficient of the twelve-loop ($n=16$) anti-prism is found to be $-42$ by a local analysis of the bootstrap equations. We also comment on the implication of our graphical rule for the non-planar contributions.

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arXiv2024

On universal splittings of tree-level particle and string scattering amplitudes

In this paper, we study the newly discovered universal splitting behavior for tree-level scattering amplitudes of particles and strings~\cite{Cao:2024gln}: when a set of Mandelstam variables (and Lorentz products involving polarizations for gluons/gravitons) vanish, the $n$-point amplitude factorizes as the product of two lower-point currents with $n{+}3$ external legs in total. We refer to any such subspace of the kinematic space of $n$ massless momenta as "2-split kinematics", where the scattering potential for string amplitudes and the corresponding scattering equations for particle amplitudes nicely split into two parts. Based on these, we provide a systematic and detailed study of the splitting behavior for essentially all ingredients which appear as integrands for open- and closed-string amplitudes as well as Cachazo-He-Yuan (CHY) formulas, including Parke-Taylor factors, correlators in superstring and bosonic string theories, and CHY integrands for a variety of amplitudes of scalars, gluons and gravitons. These results then immediately lead to the splitting behavior of string and particle amplitudes in a wide range of theories, including bi-adjoint $\phi^3$ (with string extension known as $Z$ and $J$ integrals), non-linear sigma model, Dirac-Born-Infeld, the special Galileon, etc., as well as Yang-Mills and Einstein gravity (with bosonic and superstring extensions). Our results imply and extend some other factorization behavior of tree amplitudes considered recently, including smooth splittings~\cite{Cachazo:2021wsz} and factorizations near zeros~\cite{Arkani-Hamed:2023swr}, to all these theories. A special case of splitting also yields soft theorems for gluons/gravitons as well as analogous soft behavior for Goldstone particles near their Adler zeros.

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arXiv2024

Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations

We derive the radial action of a spinning probe particle in Kerr spacetime from the worldline formalism in the first-order form, focusing on linear in spin effects. We then develop a novel covariant Dirac bracket formalism to compute the impulse and the spin kick directly from the radial action, generalizing some conjectural results in the literature and providing ready-to-use expressions for amplitude calculations with generic spin orientations. This allows, for the first time, to find new covariant expressions for scattering observables in the probe limit up to $\mathcal{O}(G^6 s_1 s_2^4)$. Finally, we use the action-angle representation to compute the fundamental frequencies for generic bound orbits, including the intrinsic spin precession, the periastron advance and the precession of the orbital plane.

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arXiv2024

A universal splitting of string and particle scattering amplitudes

We propose a new splitting behavior of tree-level string/particle amplitudes for scalars, gluons and gravitons. We identify certain subspaces in the space of Mandelstam variables, where the universal Koba-Nielsen factor splits into two parts (each with an off-shell leg). Both open- and closed-string amplitudes with Parke-Taylor factors naturally factorize into two stringy ${\it currents}$, which implies the splitting of bi-adjoint $\phi^3$ amplitudes and via a simple deformation to unified stringy amplitudes, the splitting of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory; the same splitting holds for scalar amplitudes without color such as the special Galileon. Remarkably, if we impose similar constraints on Lorentz products involving polarizations, gluon and graviton amplitudes in bosonic string and superstring theories also split into two (stringy) currents. A special case of the splitting implies soft theorems, and more generally it extends recently proposed smooth splittings and new factorizations near zeros to all these theories.

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arXiv2023

Boundary to bound dictionary for generic Kerr orbits

We establish a new relation between classical observables for scattering and bound orbits of a massive probe particle in a Kerr background. We find an exact representation of the Hamilton-Jacobi action in terms of the conserved charges which admits an analytic continuation, both for the radial and polar contribution, for a general class of geodesics beyond the equatorial case. Remarkably, this allows to extend the boundary to bound dictionary and it provides an efficient method to compute the deflection angles and the time delay for scattering orbits, as well as frequency ratios for bound orbits, in the probe limit but at all orders in the perturbative expansion.

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arXiv2022

Classical Double Copy of Spinning Worldline Quantum Field Theory

We study the classical double copy of massive spinning objects in the worldline quantum field theories (WQFT) formalism. We couple the $\mathcal{N}=1$ supersymmetric model to a Yang-Mills background to describe the propagation of a spin-half particle interacting with gluons. At the classical level, this model captures physical effects up to linear order in spin. We propose a double copy relation to map the spin tensors to the gravitation side. Enforcing R-symmetry and supersymmetry (SUSY) on the double copy integrands, we find that the gravitational theory is the ${\cal N}=2$ particle coupled to dilaton-gravity (DG). We check the double copy prescription for the eikonal phase up to next-to-leading order and for radiation at leading order in coupling constants, finding that the Grassmann nature of the spin tensor in WQFT plays a crucial role in finding full agreement with direct calculation in the $\mathcal{N}=2$ model. We show how to deform the SUSY charges of the free theory to include DG. Since the constraints algebra is first class, the worldline model can be quantized, describing the propagation of a massive vector field coupled to DG, in agreement with the literature. In addition, we investigate the double copy without preserving SUSY and R-symmetry, finding that the B-field also couples to the~worldline.

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arXiv2022

All-multiplicity amplitudes with four massive quarks and identical-helicity gluons

We explore the on-shell recursion for tree-level scattering amplitudes with massive spinning particles. Based on the factorization structure encoded in the same way by two different recursion relations, we conjecture an all-multiplicity formula for two gauged massive particles of arbitrary spin and any number of identical-helicity gluons. Specializing to quantum chromodynamics (QCD), we solve the on-shell recursion relations in the presence of two pairs of massive quarks and an arbitrary number of identical-helicity gluons. We find closed-form expressions for the two distinct families of color-ordered four-quark amplitudes, in which all gluons comprise a single color-adjacent set. We compare the efficiency of the numerical evaluation of the two resulting analytic formulae against a numerical implementation of the off-shell Berends-Giele recursion. We find the formulae for both amplitude families to be faster for large multiplicities, while the simpler of the two is actually faster for any number of external legs. Our analytic results are provided in a computer-readable format as two ancillary files.

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arXiv2021

Geodesics From Classical Double Copy

We extend the Kerr-Schild double copy to the case of a probe particle moving in the Kerr-Schild background. In particular, we solve Wong's equations for a test color charge in a Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on the equatorial plane for the potential generated by a rotating disk of charge known as the single copy of the $\text{Kerr}$ background ($\sqrt{\text{Kerr}}$). The orbits, as the corresponding geodesics on the gravity side, feature elliptic, circular, hyperbolic and plunge behaviour for the charged particle. We then find a new double copy map between the conserved charges on the gauge theory side and the gravity side, which enables us to fully recover geodesic equations for Schwarzschild and Kerr. Interestingly, the map works naturally for both bound and unbound orbits.

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arXiv2021

Classical Double Copy of Worldline Quantum Field Theory

The recently developed worldline quantum field theory (WQFT) formalism for the classical gravitational scattering of massive bodies is extended to massive, charged point particles coupling to bi-adjoint scalar field theory, Yang-Mills theory, and dilaton-gravity. We establish a classical double copy relation in these WQFTs for classical observables (deflection, radiation). The bi-adjoint scalar field theory fixes the locality structure of the double copy from Yang-Mills to dilaton-gravity. Using this the eikonal scattering phase (or free energy of the WQFT) is computed to next-to-leading order (NLO) in coupling constants using the double copy as well as directly finding full agreement. We clarify the relation of our approach to previous studies in the effective field theory formalism. Finally, the equivalence of the WQFT double copy to the double copy relation of the classical limit of quantum scattering amplitudes is shown explicitly up to NLO.

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arXiv2021

Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions

We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN and outline the generalization to $G^2v^{2n}$. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their $ε$-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space.

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arXiv2019

The Double Copy of Massive Scalar-QCD

We construct the gravitational theory emerging from the double-copy of massive scalar quantum chromodynamics in general dimensions. The resulting two-form-dilaton-gravity theory couples to flavored massive scalars gravitationally and via the dilaton. It displays scalar self-interaction terms of arbitrary even order in the fields but quadratic in derivatives. We work out the emerging Lagrangian explicitly up to the sixth order in scalar fields and propose an all order form.

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