arXiv subjects

Andrea Puhm

Publications and source records attributed to Andrea Puhm.

At least 19 recordsLinked to original sources

arXiv2026

Long-Range Interactions in Celestial CFT

Loop corrections in QED and gravity have recently been conjectured to give rise to an infinite tower of logarithmic soft theorems governing the universal low-energy behavior of photons and gravitons. We explore the implications of this tower for celestial CFT and for the algebra of conformally soft operators. The symmetry-governed part of the tower of logarithmic soft factors is shown to exponentiate, which demonstrates that these loop effects do not represent independent multi-particle interactions, but instead are rooted in the long-range exchange of gauge bosons between pairs of hard operator insertions. We define conformally soft loop operators, and compute their operator product expansions on the celestial sphere. The associated Ward identities exhibit characteristic non-local behaviors, which reflect the pair-wise interactions between hard operator insertions mediated by gauge bosons. We comment on the implications of these results for the soft operator algebra at loop order.

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arXiv2025

Exact Infrared Triangle in Massless sQED with Long-range Interactions

The logarithmic soft photon theorem in four spacetime dimensions encodes an infinite-dimensional asymptotic symmetry which acts on massive matter as a divergent superphaserotation. Here we extend this result to massless matter which is both more subtle and surprising. We derive the charge associated to divergent superphaserotations and show that it exactly vanishes to all orders in the electromagnetic coupling. This is in agreement with the vanishing of the classical logarithmic soft photon theorem which is one-loop exact. Special care is required for massless matter due to potential collinear divergences which, as we show, do however not affect the superphaserotation charge. We furthermore compute the infrared corrections to the charge associated to the subleading tree-level soft photon theorem. As a corollary of our result, we find that the tail to the velocity kick memory due to the long-range interactions between soft electromagnetic radiation and massless matter vanishes.

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arXiv2024

The Classical Super-Rotation Infrared Triangle

The universality of gravitational scattering at low energies and large distances encoded in soft theorems and memory effects can be understood from symmetries. In four-dimensional asymptotically flat spacetimes the infinite enhancement of translations, extending the Poincar\'e group to the BMS group, is the symmetry underlying Weinberg's soft graviton theorem and the gravitational displacement memory effect. Beyond this leading infrared triangle, loop corrections alter their nature by introducing logarithms in the soft expansion and late time tails to the memory, and this persists in the classical limit. In this work we give the first complete description of an `infrared triangle' where the long-range nature of gravitational interactions is accounted for. Building on earlier results in 2403.13053 where we derived a novel conservation law associated to the infinite dimensional enhancement of Lorentz transformations to superrotations, we prove here its validity to all orders in the gravitational coupling and show that it implies the classical logarithmic soft graviton theorem of Saha-Sahoo-Sen in 1912.06413. We furthermore extend the formula for the displacement memory and its tail from particles to fields, thus completing the classical superrotation infrared triangle.

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arXiv2024

The Classical Super-Phaserotation Infrared Triangle

The universality of the logarithmic soft photon theorem in four dimensions can be traced to an infinite-dimensional asymptotic symmetry which acts as a local phase rotation on matter as we have shown in 2403.13053. Here we extend our earlier results for the charges associated to these superphaserotations to all orders in the coupling and prove that their conservation is exactly the classical logarithmic soft photon theorem discovered by Saha, Sahoo and Sen in 1912.06413. We furthermore generalize the formulae for the associated electromagnetic displacement memory and its tail from particles to scalar matter fields. This completes the classical superphaserotation infrared triangle.

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arXiv2024

Size and Shape of Rotating Strings and the Correspondence to Black Holes

In light of the correspondence between black holes and fundamental strings with non-zero spin, we compute the sizes of rotating strings for small, moderate, and large values of the angular momentum and compare them to the sizes of rotating black holes. We argue that the ratio of the size perpendicular to the rotation plane to the size along the rotation plane is an approximate adiabatic invariant and can therefore be meaningfully compared for objects on different sides of the correspondence point. We show that the spin-dependence of this ratio for small angular momenta agrees for black holes and strings. When the spin is large, the ratios for these objects exhibit different behavior, but this is expected since for large angular momenta there is no direct correspondence between black holes and single-string states. We also develop a random-walk model that describes highly excited strings and accurately reproduces the sizes of rotating strings for all values of angular momentum.

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arXiv2024

Celestial amplitudes on electromagnetic backgrounds: T-duality from S-duality

What is the boundary holographic dual of S-duality for gauge theories in asymptotically flat space-times? Celestial amplitudes, by virtue of exhibiting holographic properties of the S-matrix, appear well-suited for studying this question. We scatter electrically and magnetically charged massless scalars off non-trivial electromagnetic potentials such as shockwaves, spin-one conformal primary waves, conformally soft modes and their magnetic duals which we construct. This reveals an intricate relation between conformally soft solutions, descendant CFT three-point functions and, by means of the two-dimensional shadow transform, CFT two-point functions. By comparing celestial amplitudes on electric and magnetic dual backgrounds, we provide evidence that the four-dimensional flat-space holographic dual of S-duality in Abelian gauge theory is two-dimensional T-duality. Moreover, we demonstrate that for two-dimensional boundary actions describing low-energy sectors of the bulk gauge theory, S-duality can be explicitly implemented as a T-duality transformation. We show that the Dirac quantisation condition guarantees gauge invariance in the eikonal re-summation for scattering from potentials which for magnetic scalars can be expressed in terms of 't Hooft loops.

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arXiv2024

Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity

Gauge theories and perturbative gravity in four dimensions are governed by a tower of infinite-dimensional symmetries which arise from tree-level soft theorems. However, aside from the leading soft theorems which are all-loop exact, subleading ones receive loop corrections due to long-range infrared effects which result in new soft theorems with logarithmic dependence on the energy of the soft particle. The conjectured universality of these logarithmic soft theorems to all loop orders cries out for a symmetry interpretation. In this letter we initiate a program to compute long-range infrared corrections to the charges that generate the asymptotic symmetries in (scalar) QED and perturbative gravity. For late-time fall-offs of the electromagnetic and gravitational fields which give rise to infrared dressings for the matter fields, we derive finite charge conservation laws and show that in the quantum theory they correspond precisely to the first among the infinite tower of logarithmic soft theorems. This symmetry interpretation, by virtue of being universal and all-loop exact, is a key element for a holographic principle in spacetimes with flat asymptotics.

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arXiv2023

The correspondence between rotating black holes and fundamental strings

The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states that seemingly cannot be matched to any black hole. Conversely, there exist black holes with arbitrarily large spins that cannot correspond to any single-string state. We discuss in detail the properties of both types of objects and find that a correspondence that resolves the puzzles is possible by adding dynamical features and non-stationary configurations to the picture. Our scheme incorporates all black hole and string phases as part of the correspondence, save for one outlier which remains enigmatic: the near-extremal Kerr black hole. Along the way, we elaborate on general aspects of the correspondence that have not been emphasized before.

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arXiv2023

Celestial open strings at one-loop

We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on $α'$ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted by three units with respect to tree-level, thus making manifest that the dimensionless parameter $g_{10}^2/α'^3$ organizes the loop expansion in the celestial basis.

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arXiv2023

Symmetries in Celestial CFT$_d$

We use tools from conformal representation theory to classify the symmetries associated to conformally soft operators in celestial CFT (CCFT) in general dimensions $d$. The conformal multiplets in $d>2$ take the form of celestial necklaces whose structure is much richer than the celestial diamonds in $d=2$, it depends on whether $d$ is even or odd and involves mixed-symmetric tensor representations of $SO(d)$. The existence of primary descendants in CCFT multiplets corresponds to (higher derivative) conservation equations for conformally soft operators. We lay out a unified method for constructing the conserved charges associated to operators with primary descendants. In contrast to the infinite local symmetry enhancement in CCFT${}_2$, we find the soft symmetries in CCFT${}_{d>2}$ to be finite-dimensional. The conserved charges that follow directly from soft theorems are trivial in $d>2$, while non-trivial charges associated to (generalized) currents and stress tensor are obtained from the shadow transform of soft operators which we relate to (an analytic continuation of) a specific type of primary descendants. We aim at a pedagogical discussion synthesizing various results in the literature.

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arXiv2023

The SAGEX Review on Scattering Amplitudes

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.

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arXiv2022

Celestial holography on Kerr-Schild backgrounds

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

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arXiv2022

The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes

The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries. This connection has led to a deeper understanding of the symmetries of gauge and gravitational theories and to a reformulation of scattering amplitudes in a basis of boost eigenstates which makes manifest the two-dimensional global conformal symmetry of the celestial sphere. The recast, or celestial, amplitudes possess many of the properties of conformal field theory correlation functions which has suggested a path towards a holographic description of asymptotically flat spacetimes. In this review we consider these interconnected developments in our understanding of soft theorems, asymptotic symmetries and conformal field theory with a focus on the structure and symmetries of the celestial amplitudes and their holographic interpretation.

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arXiv2022

Goldilocks Modes and the Three Scattering Bases

We consider massless scattering from the point of view of the position, momentum, and celestial bases. In these three languages different properties of physical processes become manifest or obscured. Within the soft sector, they highlight distinct aspects of the infrared triangle: quantum field theory soft theorems arise in the limit of vanishing energy $ω$, memory effects are described via shifts of fields at the boundary along the null time coordinate $u$, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension $Δ$. We focus on the subleading soft theorems at $Δ=1-s$ for gauge theory $(s=1)$ and gravity $(s=2)$ and explore how to translate the infrared triangle to the celestial basis. We resolve an existing tension between proposed overleading gauge transformations as examined in the position basis and the `Goldstone-like' modes where we expect celestial symmetry generators to appear. In the process we elucidate various order-of-limits issues implicit in the celestial formalism. We then generalize our construction to the tower of $w_{1+\infty}$ generators in celestial CFT, which probe further subleading-in-$ω$ soft behavior and are related to subleading-in-$r$ vacuum transitions that measure higher multipole moments of scatterers. In the end we see that the celestial basis is `just right' for identifying the symmetry structure.

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arXiv2021

Double Copy for Celestial Amplitudes

Celestial amplitudes which use conformal primary wavefunctions rather than plane waves as external states offer a novel opportunity to study properties of amplitudes with manifest conformal covariance and give insight into a potential holographic celestial CFT at the null boundary of asymptotically flat space. Since translation invariance is obscured in the conformal basis, features of amplitudes that heavily rely on it appear to be lost. Among these are the remarkable relations between gauge theory and gravity amplitudes known as the double copy. Nevertheless, properties of amplitudes reflecting fundamental aspects of the perturbative regime of quantum field theory are expected to survive a change of basis. Here we show that there exists a well-defined procedure for a celestial double copy. This requires a generalization of the usual squaring of numerators which entails first promoting them to generalized differential operators acting on external wavefunctions, and then squaring them. We demonstrate this procedure for three and four point celestial amplitudes, and give an argument for its validity to all multiplicities.

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arXiv2021

Conformally Soft Fermions

Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin $s=\frac{1}{2}$ and $\frac{3}{2}$ conformal primary wavefunctions with definite SL(2,$\mathbb{C}$) conformal dimension $Δ$ and spin $J$ where $|J|\leq s$. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with $Δ=\frac{1}{2}$ and its shadow with $Δ=\frac{3}{2}$ which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.

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arXiv2021

Revisiting the Conformally Soft Sector with Celestial Diamonds

Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.

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arXiv2021

Celestial Diamonds: Conformal Multiplets in Celestial CFT

We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin $s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ we classify and construct all SL(2,$\mathbb{C}$) primary descendants which are organized into 'celestial diamonds'. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,$\mathbb{C}$) conformal dimension $Δ$ and spin $J$. Radiative conformal primary wavefunctions have $J=\pm s$ and give rise to conformally soft theorems for special values of $Δ\in \frac{1}{2}\mathbb{Z}$. They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have $|J|\leq s$. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

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