arXiv subjects

Yu-tin Huang

Publications and source records attributed to Yu-tin Huang.

At least 19 recordsLinked to original sources

arXiv2026

An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers

We develop an on-shell description of low-frequency gravitational waveforms from black-hole mergers beyond leading order. Treating the strongly coupled merger as effective hard $S$-matrix data, we organize its long-wavelength response using soft theorems and the KMOC formalism. At next-to-leading order, the quantum soft theorem contains logarithmic terms absent from the classical soft theorem. We show that these extra terms cancel in the full KMOC in-in observable between the one-loop radiative amplitude and the corresponding graviton cut, leaving precisely the classical logarithmic contributions associated with gravitational drag and early-time acceleration. We also identify the $1/\omega$ corrections from remnant recoil and Christodoulou non-linear memory. These results reveal a hierarchy of merger information accessible at low frequency: logarithmic tails depend only on asymptotic hard data, recoil probes total radiated momentum, while non-linear memory probes the angular distribution of the emitted radiation.

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arXiv2026

Causality and the Equivalence Principle for Higher Energy Scattering

Recently, it was proposed that the leading high-energy behavior of scattering amplitudes is universal, independent of charge, thereby extending the equivalence principle beyond the graviton pole. In this Letter, we derive a sharper causality constraint on such behavior by studying the Regge limit of colored scattering. Parameterizing a trajectory by $s^{\alpha(t)}$ with $\alpha(0)=2-\delta$, we analyze the Shapiro/Wigner--Smith time-delays in the irreducible scattering channels. We show that any non-singlet trajectory with $\delta< 1/2$ produces a growing sign-indefinite time-delay (with $\delta=1/2$ a marginal, dimension-dependent case), which becomes dominant in the Regge diffusion region in the weak-gravity regime. The essential point is that, while the eikonal phase is naturally organized in $t$-channel irreducible representations, the physical time-delays are its eigenvalues in the $s$-channel. A non-singlet exchange therefore recouples into the physical channels with both signs, inevitably producing a negative time-delay in at least one channel.

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arXiv2026

Beyond Discontinuities: Cosmological WFCs and the Supersymmetric Orthogonal Grassmannian

We construct an $\mathcal N=2$ supersymmetric Grassmannian representation of tree-level wavefunction coefficients (WFCs) by combining Grassmannian representations of energy discontinuities with an inversion formula. Since the orthogonal Grassmannian captures homogeneous solutions of the spinor conformal Ward identities, while current WFCs satisfy inhomogeneous Ward identities, the full WFC is obtained by reconstructing the energy-dependent prefactors from a basis of discontinuities. We first demonstrate this mechanism at three points, where the triple discontinuity determines the transverse current WFC and admits a supersymmetric uplift. At four points, we invert a spanning set of five current discontinuities and embed the result in momentum superspace using super-orthogonal-Grassmannian invariants generated by $\hat\delta(C\Omega\Xi^I)$. This yields the full four-point super WFC in Grassmannian form. We show that the two orthogonal-Grassmannian branches organize distinct supersymmetric invariants and reduce, in the flat-space limit, to different helicity superamplitudes.

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arXiv2025

Flat space Fermionic Wave-function coefficients

In this work we analyze the analytic structure of tree-level flat-space wavefunction coefficients (WFCs), with particular attention to fermionic operators, and derive cutting rules for internal-fermion lines. Building on these results, we set up an iterative procedure that, starting from the flat-space S-matrix, reconstructs the 3- and 4-point WFCs with the correct partial- and total-energy poles and satisfying the requisite cutting rules. Consequently, the "four-particle test" for flat-space WFCs imposes no additional constraints beyond the consistency of the flat-space S-matrix.

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arXiv2025

Fermionic Boundary Correlators in (EA)dS space

In this paper we bootstrap de Sitter wavefunction coefficients (WFCs) involving fermionic operators. Starting with a fixed total-energy pole order, we systematically impose the conformal Ward identities (CWI) together with cutting-rule constraints. We derive the relevant cutting rules for fermionic exchange for the first time, enabling a complete determination of fermionic three- and four-point WFCs. We show that CWI fixes the leading total-energy-pole residue to the flat-space amplitude and subleading residues to curvature induced corrections to bulk vertices. The structure of the Ward-Takahashi identities are similarly fully determined. As an application, we derive four massless spin-1/2 WFC due to graviton exchange. We also revisit the tension between conserved spin-3/2 operators and de Sitter geometry. We demonstrate that the reality conditions appropriate to dS and Euclidean AdS (EAdS) lead to distinct three-point WFCs for two spin-3/2 operators and the stress tensor. Consequently, the residue of the leading total-energy pole for the four-point WFC receives graviton- and photon-exchange contributions with opposite signs in dS, whereas they appear with the same sign in EAdS. This result is reminiscent of the classic analysis by Pilch, van Nieuwenhuizen, and Sohnius, though formulated in an on-shell framework.

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arXiv2025

Bootstrapping non-unitary CFTs

We introduce a non-unitary-compatible numerical bootstrap strategy based on the statistical stability of OPE data inferred from crossing at multiple cross-ratios. For a trial spectrum, crossing determines OPE coefficients whose residual cross-ratio dependence directly measures the truncation error. This defines a scalar objective on the space of spectra, allowing bootstrap searches without imposing unitarity. Applied to two-dimensional Virasoro blocks, the method reproduces known A-series minimal models, including non-unitary examples, and yields candidate truncated solutions for c>1 with crossing violation comparable to that of minimal models. More generally, our framework provides a practical route to solving bootstrap constraints beyond the convex, unitary setting.

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arXiv2025

Surprising one-loop finiteness of 6D half-maximal supergravities

In four dimensions, it has long been established that gravity coupled to matter exhibits ultraviolet divergences at one loop, irrespective of supersymmetry. Notably, the four-matter one-loop amplitudes of half-maximal supergravity coupled to Maxwell multiplets were shown in the 1970s to be divergent. Surprisingly, we demonstrate in this work that half-maximal theories can nevertheless become one-loop finite when uplifted to higher dimensions, contrary to naive expectations. Specifically, we study the ultraviolet properties of the four-matter and two-matter two-graviton amplitudes in six-dimensional $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,1)$ supergravities, coupled to $n_T$ tensor and $n_V$ vector multiplets, respectively. We find that the one-loop amplitudes are finite for $n_T=21$ and $n_V=20$. This finiteness is unexpected, as symmetry-preserving counterterms do exist. Interestingly, both values exactly correspond to low-energy limits of type II string theories compactified on K3, which hints at possible origins to the surprising cancellations.

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arXiv2025

BDS ansatz in ABJM via scaffolding triangulations

In this work, we analyze the infrared divergence of two-loop amplitudes at arbitrary multiplicity in three-dimensional $\mathcal{N}=6$ Chern-Simons matter theory. We introduce the Bern-Dixon-Smirnov (BDS) integrand, which captures the full infrared structure while remaining free of unphysical cuts. We show that these local integrands, together with their kinematic prefactors, are naturally organized by the scaffolding triangulations of $n=2k$-gon, with distinct triangulations yielding different local representations. Remarkably, this triangulation structure also persists at the level of the integrated functions. This observation provides a graphical proof of both the cancellation of elliptic cuts and the triangulation independence of the integrated result. As a direct consequence, we obtain a simple proof that the integrated BDS integrand coincides with the one-loop maximally-helicity-violating (MHV) amplitude (the BDS ansatz) of $\mathcal{N}=4$ super Yang-Mills theory for all $n=2k$.

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arXiv2025

The Rise of Linear Trajectories

In this letter, we consider constraints on the low-energy spectrum of amplitudes with higher-spin exchange. Assuming unitarity, crossing symmetry, and super-convergent high energy behavior, reminiscent of the scattering of spin-1 and spin-2 massless helicity states, we demonstrate that the spectrum that maximizes the leading higher spin couplings of the second and third resonances is consistently given by a linear trajectory. Furthermore, for gravitational theories, the optimal spectrum is the linear trajectory defined by the mass and spin of the graviton and the lightest spin-4 resonance.

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arXiv2025

All zeros of (super)String Theory

In this paper, we study the zeros of string theory utilizing its curve-integral representation. Firstly, we note that for bosonic strings the tachyon amplitude in curve-representation is identical to the kinematic shifted Tr$\phi^3$ amplitude. Scaffolding is then equivalent to taking the OPE limit of vertex operators on the string world-sheet, which yields amplitude of higher excitations. Using this picture, we derive that the $n$-point level-$N$ scattering amplitude shares the same set of zeros as the $n$-point tachyon amplitude as well as those inherited from it's prescaffold image, i.e. $(2^N)n$-point. Doing the same for the super-tachyon amplitude, exposes new zeros for the open super-string, which can be viewed as the avatar of supersymmetry. Finally we also consider the gluino amplitude at four and six-points, identifying its zero and recovering super-Yang-Mills via scaffolding. Finally we consider the field theory limit of colored fermion amplitudes from the curve-integral form.

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arXiv2025

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.

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arXiv2024

On-Shell Approach to Black Hole Mergers

We develop an on-shell approach to study black hole mergers. Since, asymptotically, the initial and final states can be described by point-like spinning particles, we propose a massive three-point amplitude for the merger of two Schwarzschild black holes into a Kerr black hole. This three-point amplitude and the spectral function of the final state are fully determined by kinematics and the model-independent input about the black hole merger which is described by a complete absorption process. Using the Kosower-Maybee-O'Connell (KMOC) formalism, we then reproduce the classical conservation laws for momentum and angular momentum after the merger. As an application, we use the proposed three-point to compute the graviton emission amplitude, from which we extract the merger waveform to all orders in spin but leading in gravitational coupling. Up to sub-subleading order in spin, this matches the classical soft graviton theorem. We conclude with a comparison to black hole perturbation theory, which gives complementary amplitudes which are non-perturbative in the gravitational coupling but to leading order in the extreme mass ratio limit. This also highlights how boundary conditions on a Schwarzschild background can be used to rederive the proposed on-shell amplitudes for merger processes.

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arXiv2024

Non-analytic terms of string amplitudes from partial waves

We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II superstring amplitudes. Besides providing new results for their leading and sub-leading logarithmic contributions beyond genus one, our approach elucidates the general structure of non-analytic threshold terms. In the case of open strings, the use of orthogonal colour projectors allows us to efficiently compute all contributions from different worldsheet topologies at a given loop order.

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arXiv2024

Spectral Constraints on Theories of Colored Particles and Gravity

In this letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. We demonstrate that in the presence of gravity, crossing symmetry combined with two subtraction sum rules, leads to stringent constraints on the spectrum of its ultraviolet (UV) completion. Such constraints come in the form of necessary conditions on the symmetry group irreps of the UV states. This is in sharp contrast with non-gravitational theories where anything goes. Beautifully, the graviton pole is the anchor of our argument, not an obstruction. Using numerical methods, we also demonstrate that the massless spin-2 must be a singlet under said symmetry group.

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arXiv2024

All-loop geometry for four-point correlation functions

In this letter, we consider a positive geometry conjectured to encode the loop integrand of four-point stress-energy correlators in planar $\mathcal{N}=4$ super Yang-Mills. Beginning with four lines in twistor space, we characterize a positive subspace to which an $\ell$-loop geometry is attached. The loop geometry then consists of $\ell$ lines in twistor space satisfying positivity conditions among themselves and with respect to the base. Consequently, the $\textit{loop geometry}$ can be viewed as fibration over a $\textit{tree geometry}$. The fibration naturally dissects the base into chambers, in which the degree-$4 \ell$ loop form is unique and distinct for each chamber. Interestingly, up to three loops, the chambers are simply organized by the six ordering of $x^2_{1,2}x^2_{3,4}$, $x^2_{1,4}x^2_{2,3}$ and $x^2_{1,3}x^2_{2,4}$. We explicitly verify our conjecture by computing the loop-forms in terms of a basis of planar conformal integrals up to $\ell=3$, which indeed yield correct loop integrands for the four-point correlator.

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arXiv2024

Anomalous Thresholds for the S-matrix of Unstable Particles

In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics are unavoidable for unstable particles. This is in contrast to stable particles, where the anomalous thresholds are due to IR physics, set by the scale of the external kinematics. As a result, any dispersive representation for the amplitude will involve contributions from these thresholds that are not computable from the IR theory, and thus invalidate the general positivity bound. Indeed using toy models, we explicitly demonstrate that the four-derivative couplings for unstable particles can become negative, violating positivity bounds even for non-gravitational theories. Along the way, we show that contributions from anomalous thresholds in a given channel can be captured by the double discontinuity of that channel.

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arXiv2024

The 2PM Hamiltonian for binary Kerr to quartic in spin

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.

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arXiv2024

The Geometry of the Modular Bootstrap

We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment curves on $R^+{\otimes}\mathbb{Z}$, with boundaries characterized by the total positivity of generalized Hankel matrices. We phrase the Hankel constraints as a semi-definite program, which has several advantages, such as constant computation time with increasing central charge. We derive bounds on the gap, twist-gap, and the space of Taylor coefficients themselves. We find that if the gap is above $Δ^*_{gap}$, where $\frac{c{-}1}{12}<Δ^*_{gap}< \frac{c}{12}$, all coefficients become bounded on both sides and kinks develop in the space. In the second part, we propose an analytic method of imposing the integrality condition for the degeneracy number in the spinless bootstrap, which leads to a non-convex geometry. We find that even at very low derivative order this condition rules out regions otherwise allowed by bootstraps at high derivative order.

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