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Paolo Di Vecchia

Publications and source records attributed to Paolo Di Vecchia.

At least 19 recordsLinked to original sources
arXiv2026

Eikonal Scattering of Two D0-branes with Graviton Emission

We study the emission of a massless closed-string state in the scattering of two D0-branes using the boundary-state formalism. We compute the corresponding five-point amplitudes for graviton and dilaton emission in bosonic string theory and in type II superstring theory, and analyze their field-theory limit. For nonzero impact parameter, the resulting amplitudes are reproduced by an independent calculation in the worldline formulation of the corresponding low-energy theory.

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arXiv2026

Revisiting the $U(1)$-$CP$ tension in QCD from a 1PI-action perspective

We discuss the tension one encounters in trying to solve, simultaneously, the $U(1)$ and strong-$CP$ problems in QCD with light quarks and a small $\barθ$ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action $Γ$, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on $Γ$, we prove, under minor assumptions, that $CP$ violation at small non-vanishing $\barθ$ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the $U(1)$ problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in $\barθ$.

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arXiv2025

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

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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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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 $ω^{-1}$, $\logω$, $ω(\logω)^2$ in the soft limit, $ω\to0$, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type $ω^{n-1}(\logω)^{n}$ with $n\ge 3$.

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arXiv2024

The gravitational eikonal: from particle, string and brane collisions to black-hole encounters

Motivated by conceptual problems in quantum theories of gravity, the gravitational eikonal approach, inspired by its electromagnetic predecessor, has been successfully applied to the transplanckian energy collisions of elementary particles and strings since the late eighties, and to string-brane collisions in the past decade. After the direct detection of gravitational waves from black-hole mergers, most of the attention has shifted towards adapting these methods to the physics of black-hole encounters. For such systems, the eikonal exponentiation provides an amplitude-based approach to calculate classical gravitational observables, thus complementing more traditional analytic methods such as the Post-Newtonian expansion, the worldline formalism, or the Effective-One-Body approach. In this review we summarize the main ideas and techniques behind the gravitational eikonal formalism. We discuss how it can be applied in various different physical setups involving particles, strings and branes and then we mainly concentrate on the most recent developments, focusing on massive scalars minimally coupled to gravity, for which we aim at being as self-contained and comprehensive as possible.

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arXiv2024

Angular momentum of zero-frequency gravitons

By following closely Weinberg's soft theorem, which captures the $1/ω$ pole contribution to the amplitude for soft graviton emissions ($ω<Λ$) on top of an arbitrary background hard process, we calculate the expectation value of the graviton's angular momentum operator for arbitrary collisions dressed with soft radiation. We find that the result becomes independent of the cutoff $Λ$ on the graviton's frequency, effectively localizing at $ω=0$. In this way, our result captures the contribution to the angular momentum that comes from the zero-frequency modes. Like the soft theorem, our formula has an exact dependence on the kinematics of the hard particles and is only a function of their momenta. As an example, we discuss in some detail the case of the $2 \to 2$ scattering of spinless particles in General Relativity and ${\cal N}=8$ supergravity.

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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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arXiv2022

Classical Gravitational Observables from the Eikonal Operator

We propose two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons and show how to compute from them different classical observables. In the first proposal, only genuinely propagating gravitons are included, while, in the second, zero-frequency modes are added in order to recover the effects of a static gravitational field. We first calculate the radiated energy-momentum and the change in each particle's momentum, or impulse, to 3PM order finding agreement with the literature. We then calculate the angular momentum of the gravitational field after the collision. In order to do so, we adapt the method of reverse unitarity to the presence of derivatives in the operators describing the angular momentum and reproduce the result of~\cite{Manohar:2022dea} obtained by resumming the small-velocity expansion. As a new application, we derive also the variation in each particle's angular momentum up to 3PM: calculating separately field and particle contributions allows us to check the balance laws explicitly. We also show how the eikonal operator encodes the linear-response formula of Bini-Damour by deriving the linear radiation-reaction contribution to the transverse impulse at 4PM.

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arXiv2022

The eikonal operator at arbitrary velocities I: the soft-radiation limit

Observables related to the real part of the gravitational eikonal, such as the deflection angle and time delay, have been found so far to have a smooth post-Minkowskian (PM) expansion whose validity extends from the non-relativistic to the most extreme ultra-relativistic (UR) regime, which smoothly connects with massless particle collisions. To describe gravitational radiation, the eikonal phase has to be promoted to a unitary operator for which we motivate a proposal and start discussing properties in the soft-radiation limit. A convergent PM expansion is found to only hold below an UR bound (discussed in the GR literature in the seventies) above which a different expansion is instead needed implying, in general, some non-analyticity in Newton's constant. In this extreme UR regime soft radiative observables receive contributions only from gravitons and are therefore universal. This generalises the pattern discussed in \cite{DiVecchia:2020ymx} beyond the elastic case.

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arXiv2021

The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal O(G^3)$

Using $\mathcal N=8$ supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat $\mathcal N=8$ and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

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arXiv2021

Radiation Reaction from Soft Theorems

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

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arXiv2020

Universality of ultra-relativistic gravitational scattering

We discuss the ultra-relativistic gravitational scattering of two massive particles at two-loop (3PM) level. We find that in this limit the real part of the eikonal, determining the deflection angle, is universal for gravitational theories in the two derivative approximation. This means that, regardless of the number of supersymmetries or the nature of the probes, the result connects smoothly with the massless case discussed since the late eighties by Amati, Ciafaloni and Veneziano. We analyse the problem both by using the analyticity and crossing properties of the scattering amplitudes and, in the case of the maximally supersymmetric theory, by explicit evaluation of the 4-point 2-loop amplitude using the results for the integrals in the full soft region. The first approach shows that the observable we are interested in is determined by the inelastic tree-level amplitude describing the emission of a graviton in the high-energy double-Regge limit, which is the origin of the universality property mentioned above. The second approach strongly suggests that the inclusion of the whole soft region is a necessary (and possibly sufficient) ingredient for recovering ultra relativistic finiteness and universality at the 3PM level. We conjecture that this universality persists at all orders in the PM expansion.

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arXiv2020

Second-order Post-Minkowskian scattering in arbitrary dimensions

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

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arXiv2020

A tale of two exponentiations in ${\cal N}=8$ supergravity at subleading level

High-energy massless gravitational scattering in ${\cal N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $ε$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

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arXiv2020

On the N-pion extension of the Lovelace-Shapiro model

We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear $σ$-model for $α' \rightarrow 0$ keeping $F_π$ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.

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