Searcharxiv⌕ Search

arXiv subjects

Ellis Ye Yuan

Publications and source records attributed to Ellis Ye Yuan.

At least 19 recordsLinked to original sources
arXiv2025

Symbols from Bi-Projections

We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete classification of logarithmic singularities of the integral on its principal branch, by what we call touching configurations -- a geometric relationship between the integrand singularity and linear subspaces tied to boundary elements of the integral contour. These on the one hand indicate first entries of the symbol of the integral, and on the other hand induce a special set of new integrals that we call elementary discontinuities. These elementary discontinuities are derived through an operation called bi-projection, and actual discontinuities of the integral across logarithmic branch cuts are their linear combinations. By recursively applying the same analysis to the induced integrals one can fully construct the symbol of the original integral. We explicitly show how this analysis works at one loop in a massless hexagon and a box with two massive and two massless loop propagators. This framework may naturally extend to higher-loop integrals.

hep-th↗
arXiv2025

AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM

We propose an AdS$\times$S factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations, and implement it in the supergravity limit of $\mathcal{N}=4$ super Yang-Mills. By incorporating this mechanism into Mellin space bootstrap, together with an observed $Z_2$ symmetry under AdS$\ \leftrightarrow\ $S, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This AdS\times$S bootstrap method is directly applicable to generic multi-point computation at tree level.

hep-th↗
arXiv2025

The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space

We bootstrap the first-order correction in the curvature expansion of the Virasoro-Shapiro amplitude in AdS spacetime, for arbitrary Kaluza-Klein charges of external operators. By constructing a universal ansatz based on single-valued multiple polylogarithms as well as an AdS$\times$S formalism, and matching it with the low-lying result, we derive a unified formula in terms of world-sheet integrals. Our result predicts an infinite number of Wilson coefficients that were not available in previous literature.

hep-th↗
arXiv2024

Meson correlators in 4d $\mathcal{N}=2$ SCFTs and hints for 8d structures at weak coupling

We study correlators of $\frac{1}{2}$-BPS mesons in two examples of 4d SQCDs with $\mathcal{N}=2$ superconformal symmetry in the planar limit. We focus on the weakly coupled regime and obtain one-loop corrections to $n$-point meson correlators with arbitrary operator dimensions. We show that these corrections can be resumed into generating functions which exhibit emergent 8d structures similar to the ones previously observed at strong coupling via AdS/CFT. These structures of the $\mathcal{N}=2$ theories also resemble the hidden 10d structures in 4d $\mathcal{N}=4$ SYM.

hep-th↗
arXiv2024

A differential representation for holographic correlators

We present a differential representation for holographic four-point correlators. In this representation, the correlators are given by acting differential operators on certain seed functions. The number of these functions is much smaller than what is normally seen in known examples of holographic correlators, and all of them have simple Mellin amplitudes. This representation establishes a direct connection between correlators in position space and their Mellin space counterpart. The existence of this representation also imposes non-trivial constraints on the structure of holographic correlators. We illustrate these ideas by correlators in ${\rm AdS}_5 \times {\rm S}^5$ and ${\rm AdS}_5 \times {\rm S}^3$.

hep-th↗
arXiv2023

Simplicity of AdS Super Yang-Mills at One Loop

We perform a systematic bootstrap analysis of four-point one-loop Mellin amplitudes for super gluons in $\mathrm{AdS}_5\times\mathrm{S}^3$ with arbitrary Kaluza-Klein weights. The analysis produces the general expressions for these amplitudes at extremalities two and three, as well as analytic results for many other special cases. From these results we observe remarkable simplicity. We find that the Mellin amplitudes always contain only simultaneous poles in two Mellin-Mandelstam variables, extending a previous observation in the simplest case with the lowest Kaluza-Klein weights. Moreover, we discover a substantial extension of the implication of the eight-dimensional hidden conformal symmetry, which goes far beyond the Mellin poles associated with the leading logarithmic singularities. This leaves only a small finite set of poles which can be determined on a case-by-case basis from the contributions of protected operators in the OPE.

hep-th↗
arXiv2023

AdS super gluon scattering up to two loops: A position space approach

We carry out a bootstrap study of four-point correlators in 4d $\mathcal{N}=2$ SCFTs which are dual to super Yang-Mills on $AdS_5\times S^3$. We focus on the simplest $\frac{1}{2}$-BPS operators which correspond to the super gluons in the massless current multiplet. Our computation is based on an ansatz in position space which is inspired by a hidden symmetry structure manifest in the leading terms of the Lorentzian singularities of the correlators. By using other consistency conditions, we completely fix the super gluon correlators at one and two loops in the bulk genus expansion, up to possible counterterms. Our results reveal a number of interesting properties enriched by the color structures. In particular, the implication of hidden conformal symmetry on the full super gluon reduced correlator exhibits an analogous pattern as in the $AdS_5\times S^5$ supergravity correlators recently computed up to two loops.

hep-th↗
arXiv2023

Graviton Scattering in $\mathrm{AdS}_5\times\mathrm{S}^5$ at Two Loops

We report a result for the third-order correction in $1/N$ expansion to the four-point correlator of the stress tensor multiplet in $\mathcal{N}=4$ super Yang--Mills theory at large 't Hooft coupling, which corresponds to the two-loop scattering of four gravitons in the dual $\mathrm{AdS}_5\times\mathrm{S}^5$ supergravity. This is obtained by bootstrapping an educated ansatz based on intuitions from the hidden 10-dimensional conformal symmetry.

hep-th↗
arXiv2022

Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves

We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components. At the core of this strategy is the identification of a selected stratum of discontinuities induced from the integral, together with a geometric method for computing their singularities on the principal sheet. For integrals that yield multiple polylogarithms we expect the data collected in this strategy to be sufficient for the construction of their symbols. We motivate this analysis by the Aomoto polylogarithms, and further check its validity and illustrate technical details using examples with quadric integrand singularities (which the one-loop Feynman integrals belong to). Generalizations to higher-loop integrals are commented at the end.

hep-th↗
arXiv2019

Celestial Operator Products of Gluons and Gravitons

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.

hep-th↗
arXiv2018

Loops in the Bulk

We initiate a systematic investigation of Mellin amplitudes of Witten diagrams to all loop levels, by introducing integral recursion relations among them. Focusing on the scalar effective theories in AdS with the simplest type of interactions, the integral kernel that triggers the recursion obeys universal rules. As a first application, analytic properties of a 4-point triangle diagram is analyzed with this method.

hep-th↗
arXiv2018

Simplicity in AdS Perturbative Dynamics

We investigate analytic properties of loop-level perturbative dynamics in pure AdS, with the scalar effective theories with non-derivative couplings as a prototype. Explicit computations reveal certain (perhaps unexpected) simplicity regarding the pole structure of the results, in both the Mellin amplitude and a closely related object that we call Mellin pre-amplitude. Correspondingly we propose a pair of conjectures for arbitrary diagrams at all loops, based on non-trivial evidence up to two loops (and higher loops in a special class of diagrams). We also inspect the structure of residues at poles in the physical channels for several one-loop examples up to a 4-point box, as well as a two-loop double-triangle diagram. These analyses are performed using the recursive construction of Mellin (pre-)amplitudes recently prescribed in arXiv:1710.01361, for which we provide detailed derivation and generalization in this paper. Along the way we derive a set of alternative diagrammatic rules for tree (pre-)amplitudes, which are better suited to our loop construction. On the mathematical aspect we share some new thoughts on improving the contour analysis of multi-dimensional Mellin integrals, which are the essential ingredients that make our approach practical.

hep-th↗
arXiv2017

One-Loop Integrals from Spherical Projections of Planes and Quadrics

We initiate a systematic study of one-loop integrals by investigating the connection between their singularity structures and geometric configurations in the projective space associated to their Feynman parametrization. We analyze these integrals by two recursive methods, which leads to two independent algebraic algorithms that determine the symbols of any one-loop integrals in arbitrary spacetime dimensions. The discontinuities of Feynman diagrams are shown to arise from taking certain "spherical contour" residues in Feynman parameter space, which is geometrically interpreted as a projection of the quadric surface (associated to the Symanzik polynomial at one loop) through faces of the integration region (which is a simplex). This geometry also leads to a manifestly Lorentz-invariant understanding for perturbative unitarity at one loop.

hep-th↗
arXiv2016

Factorization of Chiral String Amplitudes

We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: As found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.

hep-th↗
arXiv2016

One-Loop Corrections from Higher Dimensional Tree Amplitudes

We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n+2 particles in five dimensions, one assumes that two of them cannot be "detected" and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.

hep-th↗
arXiv2015

One-loop Scattering Equations and Amplitudes from Forward Limit

We show that the forward limit of tree-level scattering equations with two massive particles yields the SL(2,C)-covariant form of the one-loop scattering equations recently proposed by Geyer et al. We clarify several properties about these equations and the formulas at one loop. We then argue that in the bi-adjoint scalar theory, such forward limit yields the correct one-loop massless amplitudes, which leads to a new formula for the latter.

hep-th↗