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Monica Pate

Publications and source records attributed to Monica Pate.

18 recordsLinked to original sources
arXiv2026

Infinite Symmetry Algebras in Four-Dimensional Conformal Field Theories

In generic interacting four-dimensional Lorentzian conformal field theories, an infinite set of universal light-ray operators constructed from the stress tensor is shown to generate the wedge subalgebra of the loop algebra of ${\rm w}_{1+\infty}$. This algebra was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. The one-point functions of the ${\rm w}_{1+\infty}$ generators in scalar states (also known as one-point event shapes) are explicitly demonstrated to be finite and are precisely related to universal soft factors in the infinite tower of soft graviton theorems. A second universal class of light-ray operators that generates the ''$S$ algebra,'' the gauge-theoretic analog of ${\rm w}_{1+\infty}$, is also constructed and shown to have finite one-point functions in four-dimensional conformal field theories with a spin-one conserved current. Along with the details of these results, this paper presents a general classification of stress-tensor and conserved current light-ray operators by scaling dimension and Lorentz ${\rm SL}(2,\mathbb{C})$ weights, a general technique for computing commutators by Poincar\'e recursion, results for other light-ray operator algebras including a local version of the four-dimensional conformal symmetry algebra, and examples for free scalar fields.

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arXiv2026

Multi-particle Celestial Operator Product Expansions from the Boundary

In celestial holography, scattering particles in four-dimensional asymptotically flat spacetimes are dual to conformal primary field operators on the celestial sphere. Multi-particle celestial operators can be formed from regularized coincident limits of single-particle celestial operators. The singular terms in the operator product expansion of multi-particle operators are shown to be determined entirely by the singular terms in the operator product expansion between single-particle celestial operators, as expected in a standard conformal field theory. Boundary operator product expansions in celestial holography are known to be dual to subtle collinear limits of bulk scattering amplitudes. The multi-particle operator product expansions derived from standard conformal-field theoretic techniques are shown to reproduce precisely the results from the corresponding bulk collinear limits in tree-level Yang-Mills and Einstein gravity. Finally, the coefficients of multi-particle celestial operator product expansions are derived from a third complementary method that enforces bulk four-dimensional translational invariance as a global symmetry of the celestial dual. The results of all three methods agree precisely.

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arXiv2025

Light-ray Operators and the ${\rm w}_{1+\infty}$ Algebra

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of ${\rm w}_{1+\infty}$, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''$S$ algebra,'' the gauge-theoretic analog of ${\rm w}_{1+\infty}$. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.

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arXiv2025

Shadow Celestial Operator Product Expansions

The linearized massless wave equation in four-dimensional asymptotically flat spacetimes is known to admit two families of solutions that transform in highest-weight representations of the Lorentz group ${\rm SL}(2, \mathbb{C})$. The two families are related to each other by a two-dimensional shadow transformation. The scattering states of one family are constructed from standard momentum eigenstates by a Mellin transformation with respect to energy. Their operator product expansion (OPE) is directly related to collinear limits of momentum space amplitudes. The scattering states of the other family are a priori non-local on the celestial sphere and lack a standard notion of OPE. Such states appear naturally in the context of asymptotic symmetries, but their properties as operators remain largely unexplored. Here we initiate a study, to be continued in a forthcoming companion paper, of a definition of an OPE for shadow operators. We present a useful technical ingredient: the transformation of the OPE coefficients associated to collinear limits under a shadow. Our results can be used to find the coefficients of all three-point functions involving any combination of celestial and shadow primaries. An OPE block is used to account for the contribution from a primary together with its global conformal descendants, all of which contribute when deriving the shadowed OPE coefficients. Applications involving $U(1)$ currents and stress tensors as well as a chiral current algebra of soft gluons are discussed.

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arXiv2023

${\rm w}_{1+\infty}$ in 4D Gravitational Scattering

In four-dimensional asymptotically flat spacetimes, an infinite tower of soft graviton modes is known to generate the symmetry algebra of ${\rm w}_{1+\infty}$ at tree-level. Here we demonstrate that the symmetry action follows from soft graviton theorems and acts non-trivially on massive scalar particles. By generalizing previous analyses that were specifically tailored to the scattering of massless particles, our results clarify that ${\rm w}_{1+\infty}$ symmetry is a universal feature of tree-level gravitational scattering in four-dimensional asymptotically flat spacetimes and originates from minimally-coupled gravitational interactions. In addition, we show that the ${\rm w}_{1+\infty}$ symmetry acts non-diagonally on massive states by mixing an infinite number of conformal families. We also present a concrete example of non-local behavior on the celestial sphere in the presence of massive scattering states.

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arXiv2021

Celestial Holography

Celestial holography proposes a duality between the gravitational $\mathcal{S}$-matrix and correlators in a conformal field theory living on the celestial sphere. In this white paper, solicited for the 2022 Snowmass process, we review the motivation from asymptotic symmetries, fundamentals of the proposed holographic dictionary, potential applications to experiment and theory, and some important open questions.

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arXiv2021

Celestial Operator Product Expansions and ${\rm w}_{1+\infty}$ Symmetry for All Spins

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of ${\rm w}_{1+\infty}$. In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of ${\rm w}_{1+\infty}$ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

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arXiv2021

Holographic Symmetry Algebras for Gauge Theory and Gravity

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

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arXiv2020

The Soft $\mathcal{S}$-Matrix in Gravity

The gravitational $\mathcal{S}$-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the gravitational memory effect is contained as an IR safe observable within the soft $\mathcal{S}$-matrix.

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arXiv2020

Celestial Amplitudes from UV to IR

Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe $\mathcal{S}$-matrix for the scattering of hard particles.

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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.

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arXiv2019

Conformally Soft Theorem in Gauge Theory

Asymptotic particle states in four-dimensional celestial scattering amplitudes are labelled by their $SL(2,\mathbb{C})$ Lorentz/conformal weights $(h,\bar{h})$ rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving $h \to 0$ or $\bar{h} \to 0$. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.

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arXiv2018

Measuring Color Memory in a Color Glass Condensate at Electron-Ion Colliders

The color memory effect is the non-abelian gauge theory analog of the gravitational memory effect, in which the passage of color radiation induces a net relative SU(3) color rotation of a pair of nearby quarks. It is proposed that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders.

hep-ph↗
arXiv2017

Gravitational Memory in Higher Dimensions

It is shown that there is a universal gravitational memory effect measurable by inertial detectors in even spacetime dimensions $d\geq 4$. The effect falls off at large radius $r$ as $r^{3-d}$. Moreover this memory effect sits at one corner of an infrared triangle with the other two corners occupied by Weinberg's soft graviton theorem and infinite-dimensional asymptotic symmetries.

hep-th↗
arXiv2017

Color Memory

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test `quarks' initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For weak color flux the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

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arXiv2017

Soft Factorization in QED from 2D Kac-Moody Symmetry

The soft factorization theorem for 4D abelian gauge theory states that the $\mathcal{S}$-matrix factorizes into soft and hard parts, with the universal soft part containing all soft and collinear poles. Similarly, correlation functions on the sphere in a 2D CFT with a $U(1)$ Kac-Moody current algebra factorize into current algebra and non-current algebra factors, with the current algebra factor fully determined by its pole structure. In this paper, we show that these 4D and 2D factorizations are mathematically the same phenomena. The soft `tHooft-Wilson lines and soft photons are realized as a complexified 2D current algebra on the celestial sphere at null infinity. The current algebra level is determined by the cusp anomalous dimension. The associated complex $U(1)$ boson lives on a torus whose modular parameter is $τ=\frac {2πi }{e^2}+\fracθ{ 2 π}$. The correlators of this 2D current algebra fully reproduce the known soft part of the 4D $\mathcal{S}$-matrix, as well as a conjectured generalization involving magnetic charges.

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arXiv2015

New Symmetries of QED

The soft photon theorem in U(1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U(1) theories, including those with massive charged particles such as QED.

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