arXiv subjects

Francesco Alessio

Publications and source records attributed to Francesco Alessio.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational amplitudes in the Regge limit: waveforms, shock waves and unitarity cuts

Motivated by recent progress in the high-energy description of gravitational scattering, we develop a systematic Regge-theory framework for $2\to2+n$ amplitudes describing the scattering of two massive particles with $n$ graviton emissions, including spin effects. Working in the ultra-relativistic limit at leading logarithmic accuracy, the massive result smoothly reduces to its massless counterpart. We describe both quantum (Regge trajectory and BFKL $t$-channel evolution) and classical ($s$-channel multi-$H$ evolution) contributions using both an exponential representation of the S-matrix and a shock-wave formalism in light-cone quantisation. In the latter approach, gravitational Wilson lines evolve in rapidity space under a boost-invariant Hamiltonian, providing a space-time realisation of the high-energy dynamics and making contact with recent effective field theory descriptions in the forward limit. As an application, we compute the leading-logarithmic contribution to the massive spinless $2\to2$ amplitude at 5PM-2SF order, recovering the previously determined massless result, and derive the tree-level $2\to3$ amplitude and its associated scattering waveform for Kerr black holes in the ultra-relativistic limit.

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arXiv2025

Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in $t/s$. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

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arXiv2025

Searching for Kerr in string amplitudes

We continue the approach of [1] to attempt to reproduce the classical electromagnetic current of the $\sqrt{\mathrm{Kerr}}$ solution from the infinite-spin limit of a three-point amplitude with two higher-spin string states and a massless vector. We review the infinite-spin limit of three-point amplitudes along the leading Regge trajectory, which differ from $\sqrt{\mathrm{Kerr}}$, and we provide evidence that any sub-leading trajectory parallel to the leading one give the same result. We extend the above investigation to the simplest sub-leading trajectory not parallel to the leading one, containing physical states with the first two harmonics. We compute all three-point amplitudes involving two such states and a massless vector, using both covariant and DDF formalism, and we extract the associated classical infinite-spin limit. Inspired by the leading Regge case, where this limit reproduces the classical electromagnetic current sourced by a rigid rotating string, we derive new classical string solutions containing the first two harmonics and compare the currents they source to the infinite-spin amplitude of the two-harmonic state. We do not see a matching between the two approaches, and we find that the classical behaviour is instead reproduced by the amplitude involving coherent string states. We conclude this paper by discussing common patterns between the different amplitudes we considered, and we conjecture how they can be generalised to reproduce $\sqrt{\mathrm{Kerr}}$.

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arXiv2025

Dirac brackets for classical radiative observables

We introduce a new coherent state expansion of the exponential representation of the S-matrix for the classical gravitational two-body problem. By combining the Kosower-Maybee-O'Connell (KMOC) formalism with the Dirac bracket structure emerging in the classical limit, we derive compact and gauge-invariant expressions for scattering observables in the presence of radiation. This causal formulation bypasses the calculation of KMOC cuts and provides a direct link between observables and a minimal set of classical matrix elements extracted from amplitudes. We illustrate our method with several examples, including the impulse, spin kick, angular momentum, waveform and the related radiative fluxes. Finally, using our formalism we evaluate for the first time the spin kick and the change in angular momentum of each particle up to $\mathcal{O}(G^2 s_1^{j_1} s_2^{j_2})$ with $j_1+ j_2 \leq 11$.

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arXiv2024

Logarithmic soft theorems and soft spectra

Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency limit, retaining an exact dependence on the kinematics of the massive objects. This allows us to study independently the ultrarelativistic or massless limit, where we find agreement with the literature, and the small-deflection or post-Minkowskian (PM) limit, where we provide explicit results up to $\mathcal{O}(G^5)$. These confirm that the high-velocity limit of a given PM order is smoothly connected to the corresponding massless result whenever the latter is analytic in the Newton constant $G$. We also provide explicit expressions for the waveforms to order $\omega^{-1}$, $\log\omega$, $\omega(\log\omega)^2$ in the soft limit, $\omega\to0$, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type $\omega^{n-1}(\log\omega)^{n}$ with $n\ge 3$.

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arXiv2024

Infrared gravity and a celestial obstruction to monogamy constraints

We argue that gravitational interactions between particles require a departure from the conventional picture of the quantum state of a multiparticle system in terms of tensor products of one-particle states. This modification is essential in order to accommodate the existence of a new boost-like relativistic angular momentum charge which pairs of particles must carry asymptotically due to long-range effects of gravity. These findings challenge conventional assumptions, prompting a reevaluation of the constraints on quantum entanglement between particle subsystems in a black hole geometry.

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arXiv2024

Kerr binary dynamics from minimal coupling and double copy

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name "classical spin covariant derivative", that is compatible with the three-point interaction of the $\sqrt{\mathrm{Kerr}}$ solution with the gauge field. The resulting Lagrangian, beside the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double-copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM ($\mathcal{O}(G^2_N)$) $2\rightarrow 2$ scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle.

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arXiv2024

A new pairwise boost quantum number from celestial states

Infrared effects in the scattering of particles in gravity and electrodynamics entail an exchange of relativistic angular momentum between pairs of particles and the gauge field. Due to this exchange particles can carry an asymptotically non-vanishing "pairwise" boost-like angular momentum proportional to the product of their couplings to the field. At the quantum level this asymptotic angular momentum suggests the existence of a new quantum number carried by multi-particle states. We argue that such quantum number is related to a modification of the action of the generators of Lorentz transformations on multi-particle states. We derive such a modification using a group-theoretic argument based on the little group of the conformal primary basis for asymptotic states. The corresponding representation is an extension of the ordinary multi-particle Fock representation of the Poincaré group. The new multi-particle states belonging to such representation no longer factorize into tensor products of one-particle states. Viewed from a gravitational point of view, our results provide evidence for a universal breakdown of the description of multi-particle sates in terms of Fock space due to infrared back-reaction.

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arXiv2024

2PM waveform from loop corrected soft theorems

We introduce a classical version of the loop corrected soft graviton theorem and we use it to compute the universal part of the one-loop (2PM) waveform up to sub-subleading order in the energy $ω$ of the emitted graviton for spinless black-hole scattering. In particular, we compute the action of the soft operators on the classically resummed four-point amplitude, that can be written in terms of the exponential of the eikonal phase (and is therefore non-perturbative in the Newton's constant $G_N$) and then we perform the usual PM expansion in powers of $G_N$ . We find perfect agreement with the existing 2PM literature at the orders $ω^{-1}$, $\logω$ and $ω\log^2ω$, which are universal. Furthermore, we use this method to compute the universal part of the $ω\logω$ contribution to the 2PM waveform. Even if in the present analysis we limit ourselves to compute the soft 2PM waveform, our general formulae can be used to extract all universal PM orders of the terms connected with the infrared divergences, once the impulse at the corresponding precision is known. Our approach, based on the resummed eikonal amplitude, gives a unified picture of the various computations of the classical soft graviton behaviour that are present in the literature since the seminal paper by Weinberg in 1965.

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arXiv2024

Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder

We present a method for hyperspectral pixel {\it unmixing}. The proposed method assumes that (1) {\it abundances} can be encoded as Dirichlet distributions and (2) spectra of {\it endmembers} can be represented as multivariate Normal distributions. The method solves the problem of abundance estimation and endmember extraction within a variational autoencoder setting where a Dirichlet bottleneck layer models the abundances, and the decoder performs endmember extraction. The proposed method can also leverage transfer learning paradigm, where the model is only trained on synthetic data containing pixels that are linear combinations of one or more endmembers of interest. In this case, we retrieve endmembers (spectra) from the United States Geological Survey Spectral Library. The model thus trained can be subsequently used to perform pixel unmixing on "real data" that contains a subset of the endmembers used to generated the synthetic data. The model achieves state-of-the-art results on several benchmarks: Cuprite, Urban Hydice and Samson. We also present new synthetic dataset, OnTech-HSI-Syn-21, that can be used to study hyperspectral pixel unmixing methods. We showcase the transfer learning capabilities of the proposed model on Cuprite and OnTech-HSI-Syn-21 datasets. In summary, the proposed method can be applied for pixel unmixing a variety of domains, including agriculture, forestry, mineralogy, analysis of materials, healthcare, etc. Additionally, the proposed method eschews the need for labelled data for training by leveraging the transfer learning paradigm, where the model is trained on synthetic data generated using the endmembers present in the "real" data.

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arXiv2021

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

The partition function of a massless scalar field on a Euclidean spacetime manifold $\mathbb{R}^{d-1}\times\mathbb{T}^2$ and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL$(2,\mathbb{Z})$ Eisenstein series with $s=(d+1)/2$. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL$(2,\mathbb{Z})$ invariance. When the spacetime manifold is $\mathbb{R}^p\times\mathbb{T}^{q+1}$, the partition function is given in terms of a SL$(q+1,\mathbb{Z})$ Eisenstein series again with $s=(d+1)/2$. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On $\mathbb{T}^{d+1}$, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

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arXiv2021

Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes

We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.

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arXiv2021

Gravitons in a Casimir box

The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a distance d. In this setting, linearized gravity, like electromagnetism, is equivalent to two free massless scalar fields, one with Dirichlet and one with Neumann boundary conditions, which in turn may be combined into a single massless scalar with periodic boundary conditions on an interval of length 2d. When turning on a chemical potential for suitably adapted spin angular momentum, the partition function is modular covariant and expressed in terms of an Eisenstein series. It coincides with that for photons. At high temperature, the result provides in closed form all subleading finite-size corrections to the standard (gravitational) black body result. More interesting is the low-temperature/small distance expansion where the leading contribution to the partition function is linear in inverse temperature and given in terms of the Casimir energy of the system, whereas the leading contribution to the entropy is proportional to the area and originates from gravitons propagating parallel to the plates.

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arXiv2020

Modular invariance in finite temperature Casimir effect

The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell's theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

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arXiv2019

Note on the symplectic structure of asymptotically flat gravity and BMS symmetries

The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving BMS charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add "ad-hoc" boundary terms in the symplectic form. In this note we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the correct Poisson brackets between the boundary fields without any additional assumption. The same Poisson brackets are used to show that BMS charges canonically generate BMS transformations on the gravitational phase space.

gr-qc↗

arXiv2019

A fuzzy bipolar celestial sphere

We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.

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arXiv2019

On the structure and applications of the Bondi-Metzner-Sachs group

This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs group. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of asymptotic simplicity are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the Bondi-Metzner-Sachs group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the Bondi-Metzner-Sachs group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the Bondi-Metzner-Sachs invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

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arXiv2019

Asymptotic Structure and Bondi-Metzner-Sachs group in General Relativity

In this work the asymptotic structure of space-time and the main properties of the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry group of asymptotically flat space-times, are analysed. Every chapter, except the fourth, begins with a brief summary of the topics that will be dealt through it and an introduction to the main concepts. The work can be divided into three principal parts. The first part includes the first two chapters and is devoted to the development of the mathematical tools that will be used throughout all of the work. In particular we will introduce the notion of space-time and will review the main features of what is referred to as its causal structure and the spinor formalism, which is fundamental in the understanding of the asymptotic properties. In the second part, which includes the third, fourth and fifth chapters, the topological and geometrical properties of null infinity, I, and the behaviour of the fields in its neighbourhood will be studied. Particular attention will be paid to the peeling property. The last part is completely dedicated to the BMS group. We will solve the asymptotic Killing equations and find the generators of the group, discuss its group structure and Lie algebra and eventually try to obtain the Poincaré group as its normal subgroup. The work ends with a brief conclusion in which are reviewed the main modern applications of the BMS group.

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