arXiv subjects

Humberto Gomez

Publications and source records attributed to Humberto Gomez.

At least 19 recordsLinked to original sources

arXiv2026

A field-inspired derivation of open string amplitudes

We propose a new method for computing $N$-point tree-level open string amplitudes, inspired by the field-theoretical perturbiner framework and bypassing world-sheet moduli integration. The construction rests on a weak associativity condition for a point-split, on-shell product of string vertices, introducing a binary-tree prescription with all physical channels manifest. The output is a multi-parametric series representation of the partial amplitude that is amenable to mass-level truncation and, therefore, numerical implementation. Besides the Veneziano amplitude, automatically represented by a dual-channel series with one free parameter, we present its five-point generalization, involving two free parameters and matched against known results in the literature. Higher multiplicities are obtained via the same systematic branching, with no separate input.

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arXiv2026

On the amplitude expansion of gluon correlators in $\textrm{AdS}_4$

We show that tree-level gluon correlators in $\textrm{AdS}_4$ admit a natural expansion in terms of flat-space scattering amplitudes at all multiplicities. In particular, every $n$-point correlator can be decomposed into a sum over energy poles whose residues are flat-space amplitudes. The $n$-point amplitude encodes the flat-space limit while curvature corrections are captured by lower-point amplitudes with merged external data. The merging of external polarizations is recursively defined via an AdS analogue of the Berends-Giele currents, giving rise to all-multiplicity formulae which we verify against Feynman diagram computations up to five points. Crucially, our approach works at the level of full correlators rather than individual diagrams, providing an elegant and transparent alternative to conventional approaches for computing correlators in anti-de Sitter space.

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arXiv2025

On-shell representation and further instances of the 2-split behavior of amplitudes

The newly discovered splitting behavior of tree-level scattering amplitudes of particles and strings has been expressed in terms of currents containing one off-shell leg. In this work, we explain how to obtain on-shell representations of the split amplitudes in different theories. Furthermore, we show that this 2-split behavior is also verified in gauge and gravity theories involving higher-dimensional operators, thereby providing additional evidence to its universal character. As a byproduct, we also generalize the transmuting operators to amplitudes in higher-derivative theories.

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arXiv2025

A Novel On-Shell Recursive Relation

We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent kinematic variables that enables the reconstruction of amputated currents from amplitudes. As a byproduct, this new recursive structure recasts the BCJ numerators into an explicitly on-shell factorized form.

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arXiv2025

One-loop $N$-point correlators in pure gravity

In this work we propose a simple algebraic recursion for the complete one-loop integrands of $N$-graviton correlators. This formula automatically yields the correct symmetry factors of individual diagrams, taking into account both the graviton and the ghost loop, and seamlessly controlling the related combinatorics.

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arXiv2023

One-loop off-shell amplitudes from classical equations of motion

In this letter we present a recursive method for computing one-loop off-shell amplitudes in colored quantum field theories. First, we generalize the perturbiner method by recasting the multiparticle currents as generators of off-shell tree level amplitudes. After, by taking advantage of the underlying color structure, we define a consistent sewing procedure to iteratively compute the one-loop integrands. When gauge symmetries are involved, the whole procedure is extended to multiparticle solutions involving ghosts, which can then be accounted for in the full loop computation. Since the required input here is equations of motion and gauge symmetry, our framework naturally extends to one-loop computations in certain non-Lagrangian field theories.

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arXiv2022

New recursions for tree-level correlators in (Anti) de Sitter space

We present for the first time classical multiparticle solutions in Anti de Sitter space (AdS) involving scalars, gluons, and gravitons. They are recursively defined through multiparticle currents which reduce to Berends-Giele currents in the flat space limit. This construction exposes a compact definition of tree-level boundary correlators using a general prescription that removes unphysical boundary contributions. Similarly to the flat space perturbiner, a convenient gauge choice leads to a scalar basis for all degrees of freedom, while the tensor structure is exclusively captured by field theory vertices. This provides a fully automated way to compute AdS boundary correlators to any multiplicity and cosmological wavefunction coefficients after Wick-rotating to de Sitter space.

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arXiv2022

Effective Field Theories and Cosmological Scattering Equations

We propose worldsheet formulae for wavefunction coefficients of the massive non-linear sigma model (NLSM), scalar Dirac-Born-Infeld (DBI), and special Galileon (sGal) theories in de Sitter momentum space in terms of the recently proposed cosmological scattering equations constructed from conformal generators in the future boundary. The four-point integrands are assembled from simple building blocks and we identify a double copy prescription mapping the NLSM wavefunction coefficient to the DBI and sGal wavefunction coefficients, including mass deformations and curvature corrections. Finally, we compute the soft limits of these wavefunction coefficients and find that they can be written in terms of boundary conformal generators acting on contact diagrams.

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arXiv2022

Cosmological Scattering Equations at Tree-level and One-loop

We recently proposed a formula for tree-level $n$-point correlators of massive $ϕ^4$ theory in de Sitter momentum space which consists of an integral over $n$ punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of $n$-point correlators. Finally, we propose a similar formula for 1-loop $n$-point correlators in terms of an integral over $(n+2)$ punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space.

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arXiv2021

Cosmological Scattering Equations

We propose a worldsheet formula for tree-level correlation functions describing a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model for inflationary cosmology. The correlation functions are located on the future boundary of the spacetime and are Fourier-transformed to momentum space. Our formula is supported on mass-deformed scattering equations involving conformal generators in momentum space and reduces to the CHY formula for $ϕ^4$ amplitudes in the flat space limit. Using the global residue theorem, we verify that it reproduces the Witten diagram expansion at four and six points, and sketch the extension to $n$ points.

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arXiv2021

Multiparticle solutions to Einstein's equations

In this letter we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well. Our construction provides a simple layout for the computation of tree level field theory amplitudes in $D$ spacetime dimensions involving any number of gravitons and matter fields, with or without supersymmetry.

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arXiv2021

Scattering of Gravitons and Spinning Massive States from Compact Numerators

We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant $D$-dimensional tree-level $n$-point amplitudes with pairs of spinning massive particles using compact exponential numerators. We discuss how this framework allows non-integer spin extensions of recurrence relations for amplitudes developed for integer spin. Our results facilitate the on-going program for generating observables in classical general relativity from on-shell tree amplitudes through the Kawai-Lewellen-Tye relations and generalized unitarity.

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arXiv2021

The $L_{\infty}$ structure of gauge theories with matter

In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the $L_{\infty}$-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to $n$-gluons with arbitrary polarisations.

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arXiv2020

One-Loop Yang-Mills Integrands from Scattering Equations

We investigate in the context of the scattering equations, how one-loop linear propagator integrands in gauge theories can be linked to integrands with quadratic propagators using a double forward limit. We illustrate our procedure through examples and demonstrate how the different parts of the derived quadratic integrand are consistent with cut-integrands derived from four-dimensional generalized unitarity. We also comment on applications and discuss possible further generalizations.

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arXiv2019

Scalar-Graviton Amplitudes

Using the CHY-formalism and its extension to a double cover we provide covariant expressions for tree-level amplitudes with two massive scalar legs and an arbitrary number of gravitons in D dimensions. Using unitarity methods, such amplitudes are needed inputs for the computation of post-Newtonian and post-Minkowskian expansions in classical general relativity.

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arXiv2019

Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories

In this work we show how a double-cover (DC) extension of the Cachazo, He and Yuan formalism (CHY) can be used to provide a new realization for the factorization of the amplitudes involving gluons and scalar fields. First, we propose a graphic representation for a color-ordered Yang-Mills (YM) and special Yang-Mills-Scalar (YMS) amplitudes within the scattering equation formalism. Using the DC prescription, we are able to obtain an algorithm (integration-rules) which decomposes amplitudes in terms of three-point building-blocks. It is important to remark that the pole structure of this method is totally different to ordinary factorization (which is a consequence of the scattering equations). Finally, as a byproduct, we show that the soft limit in the CHY approach, at leading order, becomes trivial by using the technology described in this paper.

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arXiv2019

New Factorization Relations for Non-Linear Sigma Model Amplitudes

We obtain novel factorization identities for non-linear sigma model amplitudes using a new integrand in the CHY double-cover prescription. We find that it is possible write very compact relations using only longitudinal degrees of freedom. We discuss implications for on-shell recursion.

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arXiv2019

Scattering Equations and Factorization of Amplitudes II: Effective Field Theories

We continue the program of extending the scattering equation framework by Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply the double-cover formalism to effective field theories, with a special focus on the non-linear sigma model. A defining characteristic of the double-cover formulation is the emergence of new factorization relations. We present several factorization relations, along with a novel recursion relation. Using the recursion relation and a new prescription for the integrand, any non-linear sigma model amplitude can be expressed in terms of off-shell three-point amplitudes. The resulting expression is purely algebraic, and we do not have to solve any scattering equation. We also discuss soft limits, boundary terms in BCFW recursion, and application of the double-cover prescription to other effective field theories, like the special Galileon theory.

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