arXiv subjects

Walker Melton

Publications and source records attributed to Walker Melton.

17 recordsLinked to original sources

arXiv2026

Observing Massive Scattering from Null Infinity

Because massive particles asymptote to timelike rather than null infinity, current flat space holographic proposals such as celestial or Carrollian holography struggle to describe scattering processes with massive external states. We take a step toward addressing this limitation by studying how information about massive scattering amplitudes is carried to the late-time limit of null infinity by soft graviton radiation. We show that continuity between the boundaries of timelike and null infinity implies that the late-time limit of the Bondi mass aspect naturally acts as a detector operator for massive outgoing radiation. We further relate in-in correlation functions of the Bondi mass aspect at $\mathscr{I}^+_+$ to weighted sums of scattering cross sections, implying that an observer at $\mathscr{I}$ can extract information about massive scattering processes at late times. Finally, we interpret the Bondi mass aspect as a Carrollian stress-tensor component, and study Ward identities to constrain its two-point functions.

hep-th↗

arXiv2026

Flat Space Physics from AdS Actions

Flat spacetimes are foliated by hyperbolic slices that are geometrically three-dimensional de Sitter or anti-de Sitter spaces. As such, it is possible to construct flat space holographic dualities by applying the AdS/CFT bulk-to-boundary dictionary slice by slice. In this work, we reduce 4D actions for massless scalars in both Minkowski space and Klein space and massive scalars in Minkowski space to actions on these 3D dS and AdS slices. In both Minkowski and Klein space, the reduced theories have a continuous spectrum of fields originating from the reduction over the noncompact $x^2$ direction. These actions are linked by boundary terms arising from field configurations discontinuous across the lightcone. In the massless case, different asymptotic limits of the reduced field near the boundary of the unit hyperbolic slice replicate either light cone or null infinity limits of the field; in the massive case, only one boundary mode of the reduced field has a simple geometric interpretation.

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arXiv2025

Conformal Field Theory with Periodic Time

It is shown that time-ordered correlation functions of a unitary CFT$_2$ in 2D Minkowski space admit a single-valued, conformally-invariant extension to the Lorentzian signature torus provided that the $S^1\times S^1$ spatial and temporal radii are equal. The result extends to Lorentzian CFT$_D$ on equal-radii $S^{D-1}\times S^1$ under the assumption that branch cuts occur only when a pair of operator insertions are null separated.

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arXiv2025

Quantum Fields on Time-Periodic AdS$_3/\mathbb{Z}$

We consider a free complex massive scalar on the quotient spacetime AdS$_3/\mathbb{Z}$, which has the isometry group SO(2,2) rather than its universal cover. This problem is of interest as a special example of QFT on a spacetime with closed timelike curves (CTCs), as a new context in which to study generalizations of AdS/CFT and for its role in celestial holography. A basis of time-periodic solutions to the Klein-Gordon wave equation is found in terms of hypergeometric functions. They fall into a PT even and a PT odd principal series representation, rather than the more familiar highest-weight representations of the cover of SO(2,2). For masses below the Breitenlohner-Freedman (BF) bound, the modes fall on the unitary principal series. The presence of CTCs precludes the usual canonical quantization, but geometric quantization, which begins with a symplectic form on the phase space of classical solutions, is applicable. Operators, commutators, an \sot invariant vacuum and a Fock space are constructed and transform like those of a CFT$_2$. The Fock space norm is positive below the BF bound. In celestial holography, AdS$_3/\mathbb{Z}$ arises as leaves of a hyperbolic foliation of Klein space. Our analysis determines new entries in the symmetry-constrained celestial bulk-to-boundary dictionary. In particular the Klein space $\mathcal{S}$-matrix is dual to a maximally entangled state in the tensor product of two copies of the 'wedge CFT$_2$' associated to the timelike and spacelike wedges of Klein space. Translation invariance is not present in the wedge CFT$_2$ itself but emerges as a property of this maximally entangled state.

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arXiv2024

No-Boundary State for Klein Space

Analytic continuation from $(3,1)$ signature Minkowski to $(2,2)$ signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ($\mathcal{J}$) which is the product of a null line with a $(1,1)$ signature torus. The Minkowskian $\mathcal{S}$-matrix continues to a Kleinian $\mathcal{S}$-vector which in turn may be represented by a Poincar\'e-invariant vacuum state $|\mathcal{C}\rangle$ in the Hilbert space built on $\mathcal{J}$. $|\mathcal{C} \rangle$ contains all information about $\mathcal{S}$ in a novel, repackaged form. We give an explicit construction of $|\mathcal{C}\rangle$ in a Lorentz/conformal basis for a free massless scalar. $\mathcal{J}$ separates into two halves $\mathcal{J}_\pm $ which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. $|\mathcal{C}\rangle$ is shown to be a maximally entangled state in the product of the $\mathcal{J}_\pm $ Hilbert spaces.

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arXiv2024

A Celestial Dual for MHV Amplitudes

It is shown that a 2D CFT consisting of a central charge $c$ Liouville theory, a chiral level one, rank $N$ Kac-Moody algebra and a weight $-3/2$ free fermion holographically generate 4D MHV tree-level scattering amplitudes. The correlators of this 2D CFT give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-$N$ and semiclassical large-$c$ limit, according to the holographic dictionary, as a translationally-invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact AdS$_3$ Witten diagrams.

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arXiv2024

Soft Algebras for Leaf Amplitudes

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS$_3$ leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft `$S$-algebra' as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

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arXiv2023

Celestial Gluon Amplitudes from the Outside In

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D `gluon' operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

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arXiv2023

Celestial Leaf Amplitudes

Celestial amplitudes may be decomposed as weighted integrals of AdS$_3$-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

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arXiv2023

Conformal Correlators on the Lorentzian Torus

The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well-known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus $\mathcal{LT}^2$ which arises as the conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R})$ $\simeq \text{AdS}_3/\mathbb{Z}$. We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to celestial holography, for which the $\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative celestial CFT.

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arXiv2023

Hyperbolic Vacua in Minkowski Space

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter $α$-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

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arXiv2022

Deforming Soft Algebras for Gauge Theory

Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled to $F^2$. The soft gauge symmetry '$s$-algebra', compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of the $s$-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.

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arXiv2022

Celestial Amplitudes as AdS-Witten Diagrams

Both celestial and momentum space amplitudes in four dimensions are beset by divergences resulting from spacetime translation and sometimes scale invariance. In this paper we consider a (linearized) marginal deformation of the celestial CFT for Yang-Mills theory which preserves 2D conformal invariance but breaks both spacetime translation and scale invariance and involves a chirally coupled massive scalar. The resulting celestial amplitudes are completely finite (apart from the usual soft and collinear divergences) and take the canonical CFT form. Moreover, we show they can be simply rewritten in terms of AdS$_3$-Witten contact diagrams which evaluate to the well-known $D$-functions, thereby forging a direct connection between flat and AdS holography.

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arXiv2021

Celestial Feynman Rules for Scalars

Off-shell celestial amplitudes with both time-like and space-like external legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of recursion relations for off-shell momentum space amplitudes, are transformed to the celestial sphere using the split representation. For four-point celestial amplitudes, the Feynman expansion is shown to be equivalent to a conformal partial wave decomposition, providing an interpretation of conformal partial wave expansion coefficients as integrals over off-shell three-point structures. A conformal partial wave decomposition for a simple four-point $s$-channel massless scalar celestial amplitude is derived.

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arXiv2021

Conformal Block Expansion in Celestial CFT

The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D conformal blocks via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the celestial OPE coefficients.

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arXiv2021

Eigenstates of Quasi-Keplerian Self-Gravitating Particle Discs

Although quasi-Keplerian discs are among the most common astrophysical structures, computation of secular angular momentum transport within them routinely presents a considerable practical challenge. In this work, we investigate the secular small-inclination dynamics of a razor-thin particle disc as the continuum limit of a discrete Lagrange-Laplace secular perturbative theory and explore the analogy between the ensuing secular evolution -- including non-local couplings of self-gravitating discs -- and quantum mechanics. We find the 'quantum' Hamiltonian that describes the time evolution of the system and demonstrate the existence of a conserved inner product. The lowest-frequency normal modes are numerically approximated by performing a Wick rotation on the equations of motion. These modes are used to quantify the accuracy of a much simpler local-coupling model, revealing that it predicts the shape of the normal modes to a high degree of accuracy, especially in narrow annuli, even though it fails to predict their eigenfrequencies.

astro-ph.EP↗

arXiv2021

$(2,2)$ Scattering and the Celestial Torus

Analytic continuation from Minkowski space to $(2,2)$ split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS$_3$. These three components of infinity combine to an $S^3$ represented as a toric fibration over the interval. Privileged scattering states of scalars organize into $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

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