Progress in Flat Space Holography

• Ana-Maria Raclariu (University of Amsterdam)

Celestial holography proposes a duality between the gravitational S-matrix and correlators in a conformal field theory living on the celestial sphere. I will review some of the key features of this proposal, highlighting the importance of symmetries and discuss a few recent applications, including new insights into the gravitational phase space, scattering in non-perturbative backgrounds, connections to twistor theory and the flat space limit of AdS/CFT.

A Field Theory View on Spin-Magnitude Change in Orbital Evolution

• Radu Roiban (Penn State University)

An amplitudes-based approach to gravitationally-interacting spinning particles suggested that their description involves more Wilson coefficients than standard worldline approaches. In this talk we discuss the origin and physical interpretation of the additional Wilson coefficients in the simpler context of electrodynamics coupled to various higher-spin fields.

Towards gravitational scattering at fifth order in G

• Michael Ruf (UCLA)

Scattering of heavy compact objects is an important process in gravitational physics which has recently attracted interest from different communities including numerical relativity and the approach based on the graviational self-force. In the weak field limit methods from perturbation theory are admissible. In this context, the amplitudes-based framework has been instrumental in pushing the state of the art to the fourth order in perturbation theory. In this talk I will discuss recent efforts and challenges in extending these results to the next order in perturbation theory. In particular, I will present a computation in electrodynamics which marks an important step towards the ultimate goal of computing observables for gravitational scattering at the fifth order in Newton's constant.

Challenges in the Post-Minkowskian Description of the Gravitational Two-Body Problem

• Gregor Kälin

In the last few years different approaches have lead to spectacular progress in the Post-Minkowskian description of the motion and gravitational wave emission of a two-body system. Analytical results in such approaches are obtained by studying a hyperbolic encounter using tools from high energy particle physics. On our way towards higher precision and wanting to use the analytical data for bound systems we face several computational and conceptual challenges. I will first talk about challenges that we have overcome while performing these computations in our worldline description before discussing some of these challenges that we will have to overcome in the future.

Scattering of spinning black holes at 4PM order

• Gustav Mogull (AEI Potsdam)

In this talk I will review our recent calculation of the observables (impulse, spin kick, scattering angle) involved in the scattering of two spinning black holes at fourth post-Minkowskian order (G^4) using the supersymmetric Worldline Quantum Field Theory (WQFT) formalism. This will include an examination of how to perform the involved three-loop integrals with retarded propagators, and how the observables can be efficiently generated using tree-level Berends-Giele recursion.

Radiative Observables, Angular Momentum Losses and the Eikonal Operator

• Carlo Heissenberg (Uppsala University)

The classical limit of scattering amplitudes provides a convenient strategy to calculate gravitational observables associated to binary encounters. Taking this limit requires a resummation in the effective coupling, known as the eikonal exponentiation. In this talk I will discuss an operator version of this exponentiation, which combines the elastic 2-to-2 channel with inelastic 2-to-3 channels that include graviton emissions, and illustrate its structure up to O(G^3), corresponding to two loops in the 2-to-2 amplitude and one loop in the 2-to-3 amplitude. I will then apply it to calculate dissipative observables for binary encounters: the total angular momentum loss, going also beyond the point-particle limit, the individual losses of angular momentum for each colliding body, and the scattering waveforms.

Demystifying the bound to boundary correspondence with Kerr geodesics

• Maarten van de Meent (NBI)

The bound-to-boundary (B2B) correspondence allows for the translation of results obtained for scattering encounters to bound orbits and vice versa. To the uninitiated this relationship sometimes appears almost magical. In this talk we seek to understand the B2B correspondence by examining the case of a test particle interacting with a Kerr black hole. This has the distinct advantage of having access to analytic solutions that are valid to all orders in $G$, $c$, and $a$, at cost the cost of having access to only the leading order terms in the mass-ratio. Taking a more geometric view of the correspondence we find it illustrative to distinguish two separate dualities that together make up the B2B correspondence. The first relates bound geodesics around a Kerr black hole through analytic continuation to a series of scattering orbits that alternate the between the original Kerr spacetime and its negative mass counterpart. The second duality relates the scattering in the positive mass spacetime to that in the negative mass counterpart. Together the two dualities allow one to start with knowledge of just one type of scattering and recover knowledge of bound orbit dynamics. We discuss several equivalent formulations of the second duality, including as a positive/negative angular momentum duality (as in the original B2B proposal), a positive/negative eccentricity duality, and as a positive/negative gravitational coupling duality. The new found formulation of the B2B correspondence applies to fully generic (i.e. with precessing spins) binaries, and applies to both orbit averaged and local quantities.

Developing High-Precision Gravitational-Wave Models

• Alessandra Buonanno (AEI Potsdam)

Inferring astrophysical and cosmological information from gravitational-wave observations from merging black holes and neutron stars relies on accurate predictions for the two-body dynamics and gravitational radiation. To avoid wrong scientific statements due to systematics in waveform models, upcoming observational runs with existing facilities, and with future detectors on the ground and in space, will require ever more accurate and precise waveform models, which include all physical effects. I will describe what it takes to build faithful waveform models for the entire coalescence combining different analytical methods with numerical relativity, and how perturbative results from scattering-amplitude and effective-field theory techniques could be employed to improve them, helping to achieve the stringent accuracy requirements.

What's so special about black holes

• Justin Vines (UCLA)

Much recent work, from an impressively diverse array of approaches, has led to a consensus on results for the conservative dynamics of binary black holes through next-to-leading order in the post-Minkowskian (or post-Newtonian) expansion and through fourth order in each black hole's spin. Much of this work highlights how, at least through fourth order in spin, the case of a black hole is singled out among generic spinning bodies by certain special properties of its effective description, suggesting that new results for fifth and higher orders in spin may be bootstrapped by extrapolating those properties to these orders. We will first briefly review the status of confronting such conjectures with an analysis of the response of a spinning black hole to gravitational perturbations, via solutions of the Teukolsky equation [both for a small-mass-ratio two-body system (with usual self-force calculations) and for a single black hole subjected to a gravitational plane wave (computing a classical Compton amplitude)], pointing out directions for further self-force/Teukolsky calculations, and emphasizing the likely necessity to incorporate absorptive (along with conservative) dynamics into the effective descriptions in order to establish conclusive results. We will then turn to other (seemingly orthogonal) properties which appear to make spinning black hole dynamics uniquely special, concerning "hidden" conservation laws for the motion of test bodies in a background (exact) Kerr spacetime, arising from the spacetime's "hidden symmetry" (effectively, the existence of the nontrivial Killing-Yano tensor). In the simplest case, for geodesic motion (for a monopolar test/probe body) in Kerr, the hidden symmetry leads to the conservation of the well-known Carter constant, making the dynamics fully integrable. It was later shown by Rüdiger (and independently by Gibbons et al.) that, for a spinning probe (a pole-dipole test body) in Kerr, there exist a generalized Carter constant and a further constant (a certain component of the probe's spin) which are conserved to linear order in the probe's spin. We will review recent work going on to the quadrupolar order in the probe's multipole expansion, specifically considering spin-induced quadrupoles and consistently working to quadratic order in the probe's spin, finding that there are indeed still two hidden constants of motion, but only for the special case when the probe's spin-squared--quadrupole coefficient takes the value appropriate for a black hole.

Higher-spin Compton amplitudes and Kerr

• Lucile Cangemi (Uppsala University)

Higher-spin theory and massive gauge invariance can be used as input for constraining root-Kerr and Kerr amplitudes, relevant for calculating gravitational observables with spin. Elegant three-point spin-s amplitudes exist for Kerr black holes, however constructing the corresponding four-point Compton amplitudes is an open problem. In this talk, I will discuss the origin of the Kerr three-point amplitudes from a higher-spin theory perspective. Guided by higher-spin constraints and classical-limit analysis, I will propose quantum and classical tree-level Compton amplitudes relevant for root-Kerr and Kerr to all orders in spin.

One-loop scattering waveforms from a Heavy-mass Effective Field Theory

• Gabriele Travaglini (QMUL)

I will describe how using a Heavy-mass Effective Field Theory (HEFT) enables an efficient determination of the classical limit of observables in general relativity. Specifically, quantum-suppressed terms and hyper-classical corrections can be dropped from the get go, i.e. before any integrations. I will then discuss a significant application of the HEFT: the computation of the one-loop gravitational Bremsstrahlung and the associated scattering waveforms in the frequency and time domains. We will also see how HEFT amplitudes appear naturally in the KMOC approach to classical observables. Finally, I will conclude with some prospects for future work.

An on-shell approach to self-force

• Andrea Cristofoli (University of Edinburgh)

I will present an on-shell framework for studying the self-force expansion in terms of scattering amplitudes on a curved background and their classical limit. I will first introduce the self-force expansion within the context of a plane wave background, presenting the relevant on-shell building blocks required for evaluating observables, such as scattering waveforms. Following that, I will discuss the self-force expansion on Schwarzschild, focusing on the on-shell data involved and their interpretation as resummation of ordinary perturbative amplitudes in vacuum.

Testing EFTs: amplitudes, gravitational waves, and causality

• Mariana Carrillo Gonzalez (Imperial College)

In this talk, I will review different approaches to testing Effective Field Theories (EFTs). First, I will briefly review how amplitude techniques can allow us to extract classical observables during the merge of a black hole binary for generic EFTs of gravity including minimal and non-minimal couplings. In the second half of my talk, I will focus on how to obtain bounds on Wilson coefficients of EFTs from the requirement of physical principles. I will compare the strength of positivity and causality bounds and show how applying both can be a powerful tool. Both of these techniques allow us to test EFTs effectively when comparing theoretical predictions to observations.

Gauge choices, kinematic algebras, and (A)dS

• Silvia Nagy (Durham University)

Starting with the self-dual sector, I will show how the notion of a kinematic algebra can be generalised in two directions: in the absence of gauge fixing, and in the presence of a cosmological constant, and discuss possible implications for the construction of solutions in (A)dS.

Bootstrapping Cosmological Correlators

• David Stefanyszyn

I will introduce some new techniques for computing cosmological correlators that allows them to be fixed by fundamental physical principles such as symmetry, locality and unitarity. I will illustrate these new ideas by constructing the graviton four-point function in de Sitter space.

Large Deviations in the Early Universe

• Timothy Cohen

Fluctuations play a critical role in cosmology. They are relevant across a range of phenomena from the dynamics of inflation to the formation of structure. In many cases, these it is a good approximation to coarse grain these fluctuations (in the sense of a Renormalization Group flow), and they follow a Gaussian distribution as a consequence of the Central Limit Theorem. Yet, some classes of observables are dominated by rare fluctuations and are sensitive to the details of the underlying microphysics. In this talk, I will introduce the Large Deviation Principle, and will explain how it can be used to diagnose when effective approaches fail and one must instead to appeal to the microscopic description. I will illustrate this phenomenon in the context of determining the phase transition to eternal inflation, and will briefly mention applications for the distribution of scalar field fluctuations in de Sitter, and the production of primordial black holes.

Differential Equations for Cosmological Correlators

• Hayden Lee

In this talk, I will present a new mathematical perspective of cosmological correlators in FRW spacetimes. These correlators have an integral representation in boundary kinematic space, which can be obtained from a finite set of master integrals that satisfy interesting differential equations. I will describe a graphical representation of these differential equations and show how they can be derived from simple graphical rules. This allows us to reformulate bulk time evolution as an energy flow on boundary kinematics, and provides a new way to understand the analytic structure of cosmological correlators.

Formal aspects of scattering amplitudes: Lessons and challenges in 2023

• Sebastian Mizera

I will highlight a few lessons we’ve learned from the recent progress in the field of scattering amplitudes and the challenges they present.

Liouville for Yang-Mills

• Tomasz Taylor

SUSY and OPE associativity in Celestial CFT

• Akshay Yelleshpur Srikant

In this talk, I will describe the effects of loop corrections involving both massive and massless particles on OPEs in Celestial CFT. I will go on to show that OPE associativity imposes constraints on the theory which can be cleanly phrased in terms of scattering amplitudes. I will comment on the status of these constraints in supersymmetric theories and string theory.

Bootstrapping the AdS Virasoro-Shapiro amplitude

• Tobias Hansen

I will present a constructive method to compute the Virasoro-Shapiro amplitude on AdS5xS5, order by order in AdS curvature corrections. A simple toy model for strings on AdS indicates that at order k the answer takes the form of a genus zero world-sheet integral involving single-valued multiple polylogarithms of weight 3k. The coefficients in an ansatz in terms of these functions are then fixed by Regge boundedness of the amplitude, which is imposed via a dispersion relation in the holographically dual CFT. We explicitly constructed the first two curvature corrections. Our final answer reproduces all CFT data available from integrability and all localisation results, to this order, and produces a wealth of new CFT data for planar N=4 SYM theory at strong coupling.

Generalizing Polylogarithms to Riemann Surfaces of Arbitrary Genus

• Martijn Hidding

In this talk, we explore the important role played by polylogarithms in quantum field theory and string theory scattering amplitudes, along with the challenges in generalizing these functions beyond the realm of elliptic polylogarithms. As our main result, we will present a new construction of homotopy-invariant iterated integrals on a Riemann surface, applicable to any genus. Our method employs convolutions of the Arakelov Green function and holomorphic Abelian differentials to establish higher-genus equivalents of the genus-one integration kernels from the Kronecker-Eisenstein series. These kernels are combined into a flat connection, from which we build a homotopy-invariant, path-ordered exponential generating function. The coefficients of this generating function define higher-genus polylogarithms, which generalize the Brown-Levin construction beyond genus one. The resulting polylogarithms are expected to not only play a fundamental role in higher-genus computations of string amplitudes but to also find broad applications in various other areas of theoretical physics.

A measure for chaos in string scattering

• Massimo Bianchi

Scattering processes with highly excited string (HES) states are expected to be chaotic. We show that the spacing ratios of successive peaks in the angular dependence are distributed according to the $\beta$-ensemble of random matrix theory (RMT). For the scattering amplitude of an open bosonic HES state and three tachyons, we discuss the dependence of $\beta$ on the level and helicity of the HES state. Quite remarkably, the Gaussian Unitary Ensemble (GUE) with $\beta=2$, related to the distribution of the nontrivial zeros of Riemann $\zeta$ function, applies to wave scattering on a leaky torus. Finally we explore implications of the chaotic behaviour of HES in view of the string / black-hole correspondence.

Exact integrated correlators in N=4 super Yang-Mills

• Congkao Wen

Over the past few years, it has been shown that, when integrating out the spacetime dependence with a certain integration measure, some four-point correlation functions in N=4 super Yang-Mills (SYM) can be computed exactly. These quantities are called integrated correlators; they depend on the Yang-Mills coupling \tau, and transform under the S-duality symmetry of N=4 SYM theory. I will discuss some of the recent progress on these integrated correlators in this talk.

Progress in gravitational self-force theory: recent advances in modelling asymmetric binaries

• Adam Pound

As gravitational-wave detectors become more sensitive to lower frequencies, they will increasingly detect binaries with smaller mass ratios, larger spins, and higher eccentricities. In this talk I describe how gravitational self-force theory, when combined with a method of multiscale expansions, provides an ideal framework for modelling these systems. The framework proceeds from first principles while simultaneously enabling rapid generation of waveforms on a timescale of milliseconds. I discuss the state of the art in this method: nonspinning, quasicircular waveforms at second perturbative order in the mass ratio. I present progress toward extending this second-order model to include spins and to include the final merger and ringdown. I also discuss the domain of validity of these models, focusing on their accuracy for mass ratios in the intermediate regime ~1:10 to 1:100.

Higher spins: from quantum gravity to black hole scattering

• Evgeny Skvortsov

I will review the recent developments in theories with massless and massive higher spin fields, emphasizing the role of higher spin states for the quantum gravity problem and AdS/CFT correspondence in the case of massless ones (aka higher spin gravities) and for the study of black hole scattering in the case of massive ones.

Holographic Correlators for all Λs

• Charlotte Sleight

In this talk we will discuss the central role of Euclidean anti-de Sitter space in defining holographic correlation functions on Lorentzian AdS, dS and flat spaces.